Class Journal - Math 1301 (10036)

What I hear, I forget; what I see, I remember; what I do, I understand. – Kung Fu Tzu (Confucius)

One learns the thing by doing the thing; for though you think you know it,

You have no certainty until you try. – Sophocles

Session	Date	Read & Study Section	Discussion Topics	Suggested HW Exercises	Other Info
	12 - 5		Final Exam – Comprehensive Wednesday, December 5, 10 a.m. – 12:30 p.m. Bring a #2 pencil and a scientific calculator.	You should work through every problem in the Final Exam Review to help you prepare for the final exam, as well as reviewing your three semester tests.	All MyMathLab homework assignments are open for you to improve your grade until midnight Tuesday, December 4.
28	11 – 28	5.3 5.4 5.5	It is important to remember that logb (x) is undefined if x = 0 or if x is a negative number, that is, the domain of every log function only contains the positive numbers (x>0). Since logarithms are exponents, the laws of exponents can be translated into laws of logarithms. For example, the addition law of exponents a^x a^y = a^x+y, becomes the product to sum rule for logarithms logb (xy) = logb x+ logb y. And, the subtraction law of exponents a^x ÷a^y = a^x - y becomes the quotient to difference rule for logarithms logb (x÷y) = logb x - logb y. Also, the multiplication law of exponents (a^x )^y = a^x* y becomes the exponent to coefficient rule for logarithms logb (x^n ) = n logb x. Study the examples in section 5.5. A handout was given to every student with important information about the final exam review sessions and the final exam.	See below.
27	11 - 26	5.3 5.4 5.5	Section 5.3 Exponential functions have many properties: (1) the formula can be written as f(x) = Ca^x, where C and a are positive numbers, and a is different from 1; (2) the graph is always rising when the base a>1 which is called “exponential growth”, and the graph is always falling when the base 0< a<1 which is called “exponential decay”; (3) the domain is the set of all real numbers; (4) the range is the set of all positive real numbers; (5) the function is one-to-one; (6) the x-axis is a horizontal asymptote. See the summary on pages 402-403. Section 5.4 The inverse of an exponential function is a logarithm function. Logarithms are exponents, that is, y = logb x means y is the exponent on the base b that gives x. Hence, 3 = log2 8 because 3 is the exponent on the base 2 that gives 8 or in symbols 3 = log2 8 because 2^3=8. The base of a logarithm must be a positive number different from 1. The domain of a logarithm function is the set of positive real numbers. Therefore log2 (-8) is undefined because the input is not in the domain of the log function. Study the examples in section 5.3. There are two special bases for logarithms: (1) the common log has base 10 and it is written without the base, that is, log x = log10 x; (2) the natural log has base e≈2.72 and it is written as ln x = loge x. Logarithms can be used to help solve exponential equations of the form a^x = k; study the examples on page 428. Section 5.5 Since logarithms are exponents, the laws of exponents can be translated into laws of logarithms. For example, the addition law of exponents is a^x a^y = a^x+y, and the addition law of logarithms is logb (xy) = logb x+ logb y.	See below and Section 5.4 1,3-6,9,13,19-59odd,69-75odd,91,99,101,111,119,121 Section 5.5 11,17,19,25,31-47odd,61,65,67,83	MyMathLab homework is available for section 5.3 and 5.4.
26	11 - 19		Test 3 (3.2, 3.3, 4.1, 4.2, 4.4, 5.1, 5.2) Bring a pencil and a scientific calculator.		The Final Exam Review is now available: you may purchase it in the Copy Center or print it out yourself from the web site UHD Algebra Student Web Page. You will need the freely available  Adobe Acrobat Reader to view this document.
25	11 – 14	5.2 5.3	Section 5.2 Only one-to-one functions have inverse functions. The functions f and f ^-1 have many properties: (1) when these functions are composed one after the other, they undo each other, that is, (f ^-1 ◦f)(x) = x and (f ◦ f ^-1)(x) = x; (2) the graphs of these functions are symmetric about the line y = x; (3) the inputs for f are the outputs for f ^-1 and the outputs for f are the inputs for f ^-1 that is f(x) = y means f ^-1 (y) = x; (4) the domain of f is the range of f ^-1 and the range of f is the domain of f ^-1. In applications problems, to interpret an inverse function correctly, you must remember that the inputs and outputs are switched. Study example 5, page 387: the function f has input height of a person and output length of crutches, and the function f ^-1 has output height of a person and input length of crutches. Hence, f ^-1(56) = 75 means that crutches of length 56 inches are appropriate for a person 75 inches (6 ft 3 in) tall. Section 5.3 The formula of an exponential function can be written as f(x) = Ca^x, see page 400. Note that the input to an exponential function becomes an exponent in the function formula. By the rule for order of operations, to calculate f(x) = Ca^x: 1^st, you raise a to the x power and 2^nd you multiply by C. Hence 4(3)^2 = 4 * 9 = 36. If you make a table for an exponential function, as x increases by 1, to get the next y, you multiply the previous y by a. See the tables on pages 400-401.	See below.
24	11 - 12	5.2	Section 5.2 Every function matches each input with one output. But, some functions are stronger and also match each output with one input – these are called one-to-one functions. For one-to-one functions, the input is also a function of the output. This is called the inverse function and it is written as f^--1(x). The key idea is that you switch inputs and outputs to go from f to f ^-1: the inputs to f ^-1 are the outputs from f and the outputs from f ^-1 are the inputs from f^-. Carefully study the examples in section 5.2. You should practice with tables, graphs and formulas.	See below and Section 5.3 Special exponents # 1-13odd Approximate with calculator # 17, 18 Model the data # 19 Exponential function # 25, 31, 41, 43-49odd, 55, 63, 67, Applications # 99, 101
23	11 - 7	5.1 5.2	Sections 4.4 To find the x-intercepts of the polynomial function y=3x^2+5x-7 we solve the equation 3x^2+5x-7= 0. This means the number of x-intercepts and the number of real solutions to the equation are equal. Also, since the number of x-intercepts is at most the degree of the polynomial, this means the number of real solutions is at most the degree of the polynomial. So this gives you a method to determine how many real number solutions the equation has: graph the related polynomial function and count the number of x-intercepts. Sections 5.1 In the method of composition of functions, the output from one function is used as the input to another function. For example to use the output f(x) as input to the function g, we write g(f(x)) which is read as “g of f of x”. Composition of functions is also written as (g◦f)(x) which can be read as “g composition f of x”. You should practice composition for functions given by formulas and tables and graphs. Study pages 368 – 374. Note: “Get-Out-Of-Class” activity 6 was done at the end of class today.	See below and Section 5.2 Inverse actions # 1, 3, 7, 8 One-to-one functions # 13, 15, 17, 19, 23, 25, 29, 33 Find f-inverse # 45, 51, 71, 72, 77, 89, 93, 103, 107, 113	MyMathLab homework is available for section 5.1.
22	11 - 5	4.1 4.2 4.4	Sections 4.1 and 4.2 Piecewise-defined functions can include polynomial functions. Study examples 4 and 5 on page 263. After plotting a table of data (making a scatterplot), you can conjecture the degree of the polynomial function that models the data by counting the number of turning points and the number of x-intercepts. Study table 4.3 and figures 4.28 and 4.29 on page 257. The y-value of a point on the graph of a function is called a local minimum if it is the smallest y-value compared to nearby points. The y-value of a point on the graph of a function is called an absolute minimum if it is the smallest y-value compared to all points on the graph. There are similar descriptions for local maximum and absolute maximum. Study pages 245 – 247. Sections 4.4 The complex imaginary number i has the properties (1) i = √(-1) and (2) i^2 = -1. The standard form of a complex number is a + bi where a and b are real numbers. When you simplify an expression with complex numbers, you should remember to substitute -1 for i^2 and you should remember to rewrite an expression like √(-9) as 3i. Study pages 293 – 294. A quadratic equation can have complex imaginary solutions: when you use the quadratic formula, you will get a negative number under the square root. Study example 2 on page 295.	See below and Section 5.1 Combining functions # 1, 3, 7, 8, 9, 13, 15, 19, 27, 39, Composition of functions # 53, 57, 61, 63-71odd, 79 Applications # 103, 105	MyMathLab homework is available for section 4.4.
21	10 - 31	4.1 4.2	Sections 4.1 and 4.2 Constant functions, linear functions and quadratic functions are also called polynomial functions. The formula of a polynomial function can be written as a sum where each term is a single number or a number times a power of the unknown, and the power of the unknown is an integer that is not negative. This means that polynomial functions cannot have variables in a denominator and cannot have variables under a radical. See page 242-243. The highest power of the variable is called the degree of the polynomial. The graph of a polynomial function is a straight line or an unbroken curve with no sharp turning points. Intuitively, when the graph of a function is rising, we say the function is increasing on the matching interval of x-values, and when the graph of a function is falling, we say the function is decreasing on the matching interval of x-values. See page 243. At a turning point, a function is increasing on one side of the point and decreasing on the other side of the point. The degree lets you make predictions about the graph of a polynomial function: (1) a polynomial function of degree n has at most n x-intercepts; (2) a polynomial function of degree n has at most (n-1) turning points. See page 262. The end behavior of a polynomial function refers to the left end and the right end of the graph: (1) an even degree polynomial will have both ends rise when the leading coefficient is positive and will have both ends fall when the leading coefficient is negative; (2) an odd degree polynomial will have the left end fall and the right end rise when the leading coefficient is positive, and will have the left end rise and the right end fall when the leading coefficient is negative. In other words, the ends of even degree polynomials go in the same direction and the ends of odd degree polynomials go in opposite directions. See page 261.	Section 4.1 Polynomial functions # 3-9 odd Function is increasing/decreasing # 11 – 23 odd 29, 31 Turning points # 39, 41, 43, 49, 55, 57 Application # 121 Section 4.2 Turning points # 1, 5, 7, 11, 12, 13, 15 End behavior # 19, 21, 26 Conjecture degree # 41, 43 Evaluate f(x) # 69, 71, 75, 77 Application # 81 Section 4.4 Complex numbers # 1-23 odd Complex solutions # 47, 49, 51, 55 Real zeros # 63, 65	MyMathLab homework is now available for sections 4.1 and 4.2.
20	10 - 29	3.2 3.3	Section 3.2 It takes lots of practice to learn the different methods to solve a quadratic equation: by factoring; by the square root property; and by the quadratic formula. One application of quadratic equations is to find the domain of a function that has a quadratic polynomial in a denominator. Study problems 81 – 84 on page 203. Section 3.3 The intersection method (graphical method) can also be used to solve a quadratic inequality ax^2+bx+c < 0 or ax^2+bx+c > 0. For each of these problems, the left side of the inequality is the formula of a parabola and the right side is the formula of a horizontal line (x-axis). To find the solution of the inequality: 1^st, graph the parabola; 2^nd, plot the intersection points on the x-axis; 3^rd, for each interval, the parabola should always be above the x-axis or the parabola should always be below the x-axis. Finally, choose the intervals that match the given problem. Carefully study example 1 on page 207.	See below and Section 3.3 Solve graphically # 1, 5, 7, 9 Solve analytically # 11 – 17 odd Applications # 61, 63	MyMathLab homework is now available for sections 3.2 and 3.3.
19	10 - 24		Test 2 (2.1, 2.2, 2.3, 2.4, 2.5, 3.1) Bring a pencil and a scientific calculator.
18	10 - 22	3.1 3.2	Section 3.1 When a quadratic function is used in applications, the vertex provides important information: the y-coordinate is the minimum value of the function when the parabola opens upward and it is the maximum value of the function when the parabola open downward. Study Example 8 - Maximizing area, and Example 9 – Maximum height of a baseball. Section 3.2 A quadratic equation can be written as ax^2+bx+c = 0 where a cannot be zero. You can solve a quadratic equation analytically (by hand) by (1) using the method of factoring; (2) using the method of the square root property; and (3) using the method of the quadratic formula. Study example 1 and 2 (factoring), example 4 (square root property), and example 7 (quadratic formula).	Section 3.2 Solve by factoring # 1, 3, 5, 21 Solve by square root property # 11, 13, 15 Solve by quadratic formula # 19, 23 Solve by graphing # 25, 27 Solve the quadratic equation # 31, 33 Find the domain # 81, 83 Applications # 99, 105, 111
17	10 - 17	3.1	Section 3.1 Some properties of a quadratic function are: (1) the highest power of the unknown is two, and there is no variable in a denominator and there is no variable under a root; (2) the standard form is f(x)=ax^2+bx+c where a cannot be zero; (3) the graph is a parabola that opens up if the coefficient of the square term a is positive and opens down if the coefficient a is negative; (4) the tip of the parabola is called the vertex; (5) the vertical line that goes through the vertex is called the axis of symmetry. To find the coordinates (x, y) of the vertex by hand, that is analytically, you can use the vertex formula x = -b/2a and then substitute this x-value into the function formula to find the matching y-value since y=f(x). Every quadratic function has the same domain: the set of all real numbers. However, the range changes from one quadratic function to another but the y value of the vertex is either the smallest value in the range if the parabola opens up or it is the largest value in the range if the parabola opens down. There are many important applications of quadratic functions: study examples 8 and 9 on page 179-180. Note: “Get-Out-Of-Class” activity 5 was done at the end of class today.	See below.	All MyMathLab assignments for test 2 must be completed by midnight Tuesday, October 23.
16	10 - 15	2.5 3.1	Section 2.5 It takes lots of practice with piece-wise defined functions to learn and remember how to find the correct answers to questions. Carefully study the book examples and your class notes to help you with this topic. Another way to think of absolute value is “distance from zero on the number line.” For example, the solutions to the absolute value equation |x|=3 can be thought of as the numbers on the number line whose distance from zero is three. Since there are two numbers whose distance from zero is three, -3 and 3, the absolute value equation has two solutions x=+3. Similarly, the solutions to the absolute value inequality |x|<3 can be thought of as the numbers on the number line whose distance from zero is less than three. All numbers between -3 and 3 have distance from zero less than three. So the solutions to the absolute value inequality |x|<3 can be written as -3<x<3. Lastly, the solutions to the absolute value inequality |x|>3 can be thought of as the numbers on the number line whose distance from zero is greater than three. All numbers less than -3 OR greater than 3 have distance from zero more than three. So the solutions to the absolute value inequality |x|>3 can be written as x<-3 OR x>3. Carefully study example 10 on page 150. Read ahead in section 3.1 (quadratic functions).	See below and Section 3.1 Classify function # 1-7 odd, Graph properties of quadratic functions # 7 – 11 odd Equation/Formula of quadratic functions # 13 - 19odd Vertex formula # 25 – 31 odd Graph quadratic function # 59-75 odd Applications # 83, 85-88	A practice quiz for chapter 2 is now available in MyMathLab to help you review for test 2.
15	10 - 10	2.5	Section 2.5 A piece-wise defined function has 2 or more rules, but since each input can have only one output, only one rule is used at a time for a given input. Usually, each rule is used only for a specific interval of x-values. The domain is the union of all the intervals for all of the rules. The graph consists of pieces: one piece for each rule. Study examples 1, 2 and 3 on pages 141 – 143. An absolute value function can be written as a piece-wise defined function. See page 144. There are special rules for solving equations and inequalities with absolute values. Study pages 145 – 150. Note: “Get-Out-Of-Class” activity 4 was done at the end of class today.	See below.	MyMathLab homework for section 2.5 is now available.
14	10 - 8	2.4 2.5	Section 2.4 The 3-part inequality (compound inequality) a<x<b means that x must satisfy two requirements: a<x and x<b. When we solve a 3-part inequality, our goal is to isolate the variable in the middle. We use the same rules as for solving a 2-part inequality, except that we must do the same action 3 times: add the same number to each of the 3 parts; subtract the same number from each of the 3 parts; etc. Study example 6 on page 131. The graphical method (intersection method) can be used to solve an inequality. Study example 2 on page 127. In some applications (word problems), the desired answer is a range of values for the unknown: find the range of altitudes where the matching temperature is below freezing; find the range of miles that can be driven in a rental car to keep the total cost at most $100, etc. Study example 7 on page 131. Read ahead in section 2.5: piecewise-defined functions.	Section 2.5 Piecewise-defined functions # 1, 3, 7, 9, 11, 15, 19, 20, 22, Absolute value # 41, 45, 47, 51, 59, 61, 63, 67, 71, 73, 77, 79, 87, Applications # 93,103
13	10 - 3	2.3 2.4	Section 2.3 The method of graphically solving an equation (intersection method) can be used for any equation, however, note that the solutions from this method may not be exact but the solutions may only be approximate. Carefully read the recommended steps in “Solving Application Problems” on page 114. Study example 13 (mixing acid in chemistry) on page 116. Remember the rule: (part acid) ÷ (total mixture) = (percent acid). Section 2.4 The rules for solving inequalities are similar to the rules for solving equations, but there is one big difference. If you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality. Study the properties of inequalities on page 126. Note: “Get-Out-Of-Class” activity 3 was done at the end of class today.	Sectin 2.4 Interval notation # 1 – 11 odd, Solve linear inequality symbolically # 13 – 31 odd, 35, Applications 91,101	MyMathLab homework for section 2.4 is now available.
12	10 - 1	2.2 2.3	Section 2.2 You are expected to practice problems involving direct proportion and inverse proportion. Study examples 11 and 12 on page 97. Section 2.3 In a linear equation, the highest power of the unknown is one, and there is no variable in a denominator and there is no variable under a root. For a given equation, if some numbers are solutions and some numbers are not solutions, we call it a conditional equation. For a given equation, if no number is a solution, we call it a contradiction. For a given equation, if every valid number is a solution, we call it an identity. See page 107. Three methods for solving equations are (1) to solve symbolically or analytically means to solve by hand; (2) to solve graphically means to use the intersection method; (3) to solve numerically means to use tables. Study page 110 for an explanation of the intersection method.	See below.	MyMathLab homework for section 2.3 is now available.
11	9 - 26	2.2	Section 2.2 You need to practice finding the formulas of lines that are parallel or perpendicular to a given line. Study example 6, page 92, and study example 7, page 93. Vertical lines have formulas that can be written as x=k; the points on this line all have an x-coordinate equal to the value of k. Vertical lines have undefined slope. Horizontal lines have formulas that can be written as y=b; the points on this line all have a y-coordinate equal to the value of b. Horizontal lines have slope equal to zero. In applications of linear functions, the slope tells you how fast the output is changing (the rate at which the output is changing). The units on the slope are the output units per input unit. Study example 9, page 94, and problem 81, page 102. When the output quantity y is directly proportional to the input quantity x, this means the formula relating these quantities can be written as y=kx, where k is the constant of proportionality. Note that this is a special case of a linear function where the slope is the constant of proportionality and the y-intercept is zero. Study examples 11 and 12 on page 97. When the output quantity y is inversely proportional to the input quantity x, this means the formula relating these quantities can be written as y=k÷x, where k is the constant of proportionality. Note: “Get-Out-Of-Class” activity 2 was done at the end of class today.	Section 2.3 Is the equation linear? 1 – 5 odd Solve the linear equation by hand (analytical method) # 7 – 11 odd, 17 – 25 odd Contradiction, identity, conditional equation # 31- 39 odd, 44 Solve using intersection method (graphical method) # 47 – 55 odd Solve using tables (numerical method) # 65 – 73 odd Applications (problem solving) # 84, 86, 88, 96, 112
10	9 - 24	2.2	Section 2.2 There are different ways that the equation/formula of a line can be written: (a) slope-intercept form, y=mx+b, page 89; (b) point-slope form, y-y1=m(x- x1), page 88; (c) standard form, ax+by=c, page 90. You are expected to know how to find the equation/formula of a line given: (a) two points on the line, example 1, page 88; and (b) the slope of the line and one point on the line, example 2, page 89. In some problems, you must find the intercepts of a line: (a) for the x-intercept, set y=0; and (b) for the y-intercept, set x=0, example 4, page 91. Parallel lines have equal slopes; see page 92, example 6. The slopes of perpendicular lines have a product equal to negative one which also means the slope of one line is the negative reciprocal of the slope of the other line: see page 93, example 7.	Section 2.2 Find function formula # 1 – 23 odd, 24, 25, 27, 29, 31, 35, 39 – 45 odd Match equation, graph # 47 – 51 odd Find formula for function table # 53 – 57 odd Find intercepts, graph function # 59 – 75 odd Applications # 81, 84, 87 Viewing rectangle # 93 Direct variation # 99, 101, 103 - 105, 107	Test 1 was returned. You are responsible for doing your test corrections and saving your test to study from for the final exam at the end of the semester. MyMathLab homework for section 2.2 is now available.
9	9 - 19		Test 1 (1.1, 1.2, 1.3, 1.4, 2.1) Bring a pencil and a scientific calculator.
8	9 – 17	1.4 2.1	Section 1.4 A constant function is a special type of linear function: (1) the output is the same no matter the input; (2) the function formula can be written as f(x)=b where the output is constantly b for all inputs x; (3) the graph is a horizontal line; (4) the slope is zero (5) the value of y=f(x) does not change for each unit increase in the input x. See page 46. Section 2.1 In application problems where the output changes at a constant rate, the function is a linear function and the formula can be written in the form f(x)=(constant rate of change)x+(initial amount). Study examples 3, 4, 5, and 6 on pages 76-78.	See below.	MyMathLab assignments for Test 1 must be completed by midnight tomorrow, Sept. 18.
7	9 – 12	1.4 2.1	Section 1.4 We reviewed the special properties of linear functions: (1) the formula can be written in the form f(x)=ax+b or f(x)=mx+b; (2) the graph of a linear function is a straight line; (3) the coefficient of x is called the slope ; (4) interpretation of slope – What is the change in the output when there is a unit increase in the input? For example, assume the price of carpet is f(x)=20x dollars for x square yards. Here the output (price) is in dollars and the input (amount of carpet) is in square yards. How do we interpret the slope, that is, by how much does the output change when the input increases by 1? Answer: The total price increases by $20 for each additional square yard of carpet, or by $20 per sq. yd. (5) for a linear function written as a table, if the inputs are equally spaced, then the outputs are equally spaced. Section 2.1 Given two points on a line, you can find the equation/formula of the line. First, find the slope and substitute that number for m in the formula f(x)=mx+b. Second, remember that on a graph, the y-value equals the output f(x). This means you can rewrite the formula as y=mx+b. Lastly, pick one of the given points and substitute for x and y into the equation y=mx+b. Solve this equation for b and then write your answer.	Section 2.1 Match function with table # 1,2,3 Find formula for function graph # 5,8 Graph by hand # 13,15,17,23, Find formula for function # 25,27,30, Applications # 37-40, 41, 44 Find function formula for function table # 49,51	There is a practice quiz for Chapter 1 in MyMathLab.– you can use this to help you review for the test.
6	9 - 10	1.3 1.4	Section 1.3 If a function formula contains a variable in a denominator, you should solve “denominator=0” to find the numbers to omit from the domain. If a function formula contains a variable in the radicand of a square root, you should solve “radicand > 0” to find the domain. Study examples 3, 4, and 5 in section 1.3. When the value of quantity y depends on the value of quantity x, we say “quantity y is a function of quantity x” and write y = f(x). Note that “output = f(input)”or “f(input)=output”. Hence if the distance traveled d is a function of the time traveled t, we write d = f(t). Study example 7, page 37. Section 1.4 Linear functions have many special properties: (1) the formula can be written in the form f(x)=ax+b or f(x)=mx+b; (2) the graph of a linear function is a straight line; (3) the coefficient of x is called the slope ; (4) interpretation of slope – the slope gives the change in the output per unit increase in the input. Jolene’s weekly salary is given by f(x)=5x+250 dollars; the slope 5 can be interpreted as “her salary increases 5 dollars for each additional client” ; (5) for a linear function written as a table, if the inputs are equally spaced, then the outputs are equally spaced. Note: “Get-Out-Of-Class” activity 1 was done at the end of class today.	Section 1.4 Find slope given two points # 1,3,5,13 Find slope from function formula and interpret slope # 17,19,21 Application problems # 25,27,29 Recognize a linear function from a table # 31,33,34,35, 53,55, Recognize a linear function from a formula # 37,41,43,45,47,49 Write a function formula # 62,63,64,66,67 Find values from a graph and formula # 75,76,77 Other # 69,104	Online homework is now available for sections 1.1, 1.2, 1.3 and 1.4 in MyMathLab.
5	9 - 5	1.3	Section 1.3 We write f(a) is undefined when the function does not have an output (y-value) for the input x = a. For a function graph: (1) a number on the x-axis is in the domain if a vertical line through the number touches a point that is part of the graph; (2) a number on the y-axis is in the range if a horizontal line through the number touches a point that is part of the graph. The domain and range can often be written using interval notation. For example, the interval [1,3] stands for the set of all real numbers greater than or equal to 1 and less than or equal to 3, while the interval (1,∞) stands for the set of all real numbers greater than 1, and the interval (-∞,1) stands for the set of all real numbers less than 1. You should practice finding the domain and range of a function graph: work through exercises 43 – 50 on page 43. The domain of a function formula depends on the arithmetic operations in the formula: it is important to remember that division by zero is not defined. For a function formula with a variable in a denominator, you must omit a number from the domain if the number makes a denominator equal zero. Study examples 3, 4, and 5 in section 1.3.	See below.	The number of absences that you have in the course will be counted starting today since the official day of record was September 4.
4	3 - 29	1.3	Section 1.3 When a graph is a function, each vertical line will touch the graph at most once – this means each x-value (input) is matched with exactly one y-value (output). When a graph is not a function, some vertical line will touch the graph more than once - this means some x-value (input) is matched with more than one y-value (output). Function notation: When the ordered pair (a,b) is contained in a function, this means (a,b) = (x, y) = (input,output) and we express this in function notation by writing f(a)=b. Note that the input or x-value is written inside the parentheses and the output or y-value is written on the other side of the equals sign. Study the rule “Making Connections” on page 32 and example 4 on page 35. In some problems, only one value of x or y is given, and then you must find the value of the other variable. A function formula can be rewritten with empty parentheses in place of the input variable x and then the same number is substituted in the parentheses all the way across to find the matching output or y-value.	See below.	Try using the computer to make a scatter plot – click here for instructions, but only do steps 1, 2 and 3.
3	3 - 27	1.2 1.3	Section 1.2 In many application problems, it is important to determine the maximum and minimum of the x-values and of the y-values. Study example 4, page 17. Study the special notation for a viewing rectangle or graphing window on page 23: [Xmin, Xmax, Xscl] x [Ymin, Ymax, Yscl]. You should be able to predict the number of tick marks on the positive x-axis and the positive y-axis. See problems 69 – 76 on page 27. Note that for a given relation, different persons may choose different viewing rectangles. Section 1.3 Some relations are stronger than others: if each x-value (input) is matched with exactly one y-value (output) then the relation is called a function. A relation is not a function if some input has more than one output; this means repeated outputs are OK. You should learn to recognize when a table or a set of ordered pairs is a function: see example 8, page 38. You should also learn to recognize when a graph is a function; see example 9, page 39.	Section 1.3 Graph of a function # 1,3, 5,9,13,15,21 Use formula to evaluate f(x), find domain # 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35 Use graph to evaluate g(x) # 37,39,41 Use graph to estimate domain and range # 43,45,47,49 Use graph to find intercepts # 54,55,56,57 Change representation #63,64,65,69, 70, 71 Interpret in context # 75 Is it a function # 79,81, 84, 87,89,91 Applications # 97,99,105,108	Online homework is now available for sections 1.1, 1.2, and 1.3 in MyMathLab. Please work on these as the sections are discussed in class. Free math tutoring is available in the Math Lab beginning Monday, September 27.
2	8 - 22	1.1 1.2	Section 1.1 Note: (1) a rational number can be written as a ratio of integers (e.g. 4/5) or as a finite decimal (e.g. -4/5 = -0.8) or as an infinite decimal that repeats (5/3 = 1.6666666.....); (2) an irrational number cannot be written as a ratio of integers but it can be written as an infinite decimal that does not repeat (e.g. √2 = 1.414214....). A real number can be written as a decimal number and can be plotted on the number line. Study example 1 for practice in classifying numbers. Study exercises 13 – 18 on pages 10-11 which also involves classifying numbers. Section 1.2 A relation is a set of ordered pairs (x,y) – a relation may also be represented by a table or a graph. The set of all x-values is the domain of the relation; the set of all y-values is the range of the relation. See page 16. When the graph of a relation consists of distinct points, the graph is called a scatterplot. See page 18.	Section 1.2 Relation, domain, range # 9, 63,65,67 Graphing window # 71 Scatterplot # 81	Online homework is now available for sections 1.1 and 1.2 in MyMathLab. Please work on these as the sections are discussed in class. Free math tutoring is available in the Math Lab beginning Monday, September 27.
1	8 - 20	1.1	Read ahead and review the special numbers: natural numbers, integers, rational numbers, irrational numbers, real numbers – see page 2. Study example 4, page 4, for the steps in calculating percent change. A number in scientific notation has the form c × 10^n where n is an integer and 1< | c | <10. Study example 5, page 5, to review calculations written using scientific notation.	Section 1.1 Classify numbers # 1, 2, 3, 5, 7, 11,13, 15, 17 Percent change # 19, 21 Scientific notation # 25, 31, 39, 43, 53, 59, 69 Calculator # 73 Problem solving # 79, 81, 87, 91, 93	A handout with step-by-step instructions for registering in MyMathLab was given to each student. Please try to register in MyMathLab as soon as possible. After you successfully register, please start working on the HW for section 1.1.