Chapter y= x f(4)= f(x)= x a. 0 b. 3 and 0 c. x 0.5, , 9, and t

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Hugh Powers
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1 Chapter 11 Lesson (3x 2) 2 =9x 2 12x a. 228 shoppers b. 58 people/hr c. at 3:00 PM a b. 99 c. 2 d The x-coordinate of the vertex must be at x =1 because of symmetry of the parabola a+3c=56.5, a+4c=49.5, a=$15.50, c=$ a. m = 2 7, b = 2 b. m = 1 3, b = 6 c. m = 5, b = 1 d. m = 3, b = a. x 2 b. x > 1 c. x 9 d. x > a. 2 x 4 b. s11 u 2 c. 81 w 8 d. 1 m a. 3 b. 1 c. 4 d a. x 8 6x 1 2(x 6) b. = 2x 12 x 2 x a. (0, 3) b. ( 1, 0) and (3, 0) a. x 4 y 3 b. xy c. 6x 6 d. 8x 3 Lesson y= x f(4)= f(x)= x a. 10 b. 1 c. 125 d. no output because you cannot take the square root of a negative number, e. 5 f. 10 or 10 g. no input will yield a negative absolute value h. 6 i a. 0 b. 3 and 0 c. x 0.5, , 9, and t y= 4 3 x Marley is correct; they are perpendicular since the slopes are 2 7 and miles a. x+2 x 6 4x 3 b. x 5 c. x(x 6) d. x+3 x 1 x 7 e. 3x 1 x 5 x 3 f. x a. 1 4 b. 1 c = 1 25 d. 1 x 2 78 Algebra Connections

2 Lesson a. Each input (pushing a button) relates to an output (a can of soda). b. Input: possible buttons to push and money; output: possible types of soda c. No, it is not. You cannot predict the output when Lemon Twister is selected. d. Yes; Based on this information, you can predict that every time the Blast is selected, the output will be a can of Blast. e. Yes; Based on this information, you can predict that every time Slurp is selected, the output will be a Lemon Twister. f. Relations that are functions have a predictable (and unique) output value for each input value. Relations that are not functions have more than one output for at least one input, which makes them unpredictable Typical response. A function is a relation in which each input has only one output a. No; Button 2 gave two different types of candy b. Yes; each input has only one output c. No; x =2 has two different outputs d. No; at least one x-value has more than one y-value e. Yes; each x-value has only one y-value f. Yes; each x-value has only one h(x)-value g. Yes; each input has only one output No; vertical lines are not functions Some possible machines are an ATM machine, a calculator, a radio, etc , 5, u =4, v= a. 7 b. 1 c. 9 d a. x =8 or x = 2 b. x = ±7 c. x =1 or x = 3 d. x = 5 or x = a. 25a 22 b 36 b x 9 y B Answer Key 79

3 Lesson a. 2.3, 0, 3.3 b. 2, 3 c. 3.7 d. No a. 1, 2, 6 b. There is no solution because you cannot divide by zero. c. No; the error occurs when the denominator is 0, and 3 is the only value that causes that to happen. d. All numbers except x = a. Yes; each input has exactly one output. b. 2 x 4 c. 1 y 3 d. No; he is missing all the values between those numbers. The curve is continuous, so our description needs to include all the numbers, not just the integers See solutions below. a. D. 3 x 3, R. 3 y 3 b. D. <x<, R. <y< c. D. 2 x 4, R. 4 y 2 d. D. <x<, R. y 4 e. D. 2 x 4, R. 3 y 2 f. D. 2, 1, and 4, R. 4, 1, 1, and a. No; we only know that the integers used in the table worked. We do not know about the numbers between the integers or those beyond the table. b. Not quite. If we knew that f(x) was a parabola, then (0, 4) would be the vertex and then the range would be the set of numbers greater than or equal to 4. However, since we were not told the rule, that is an assumption. In fact, we cannot even assume that the relation is continuous; it could just consist of the points listed in the table. c. No a. <x< b. All y-values greater than There are many possible solutions. See example at right a. not a function as more than one y-value is assigned for x between 1 and 1inclusive b. appears to be a function c. not a function because there are two different y-values for x =7 d. function a. x-intercepts ( 1, 0) and (1, 0), y-intercepts (0, 1) and (0, 4) b. x-intercept (19, 0), y-intercept (0, 3) c. x-intercepts ( 2, 0) and (4, 0), y-intercept (0, 10) d. x-intercepts ( 1, 0) and (1, 0), y-intercept (0, 1) Marisol. y=2x, Mimi. y=3x 3, solution: x =3 hrs, so 6 miles suur No; the slope of AB is 3 5 suur, while the slope of AC is a. x = y b. y= 3 2 x 9 c. r = d t d. r = C 2 and the slope of BC suur is a. 2x 5 x 6 b. x Algebra Connections

Lesson 11.1.5 11-53. a. 4 b. 3 c. 1 d. 2 e. 6 f. 5 11-54.

4 Lesson a. 4 b. 3 c. 1 d. 2 e. 6 f (1) D: <x<, R: <y< ; (2) D: 4 x 0, R: 0 y 2 ; (3) D: all x-values except x =0, R: all y-values except y=1; (4) D: x 3, R: y 0; (5) D: <x<, R: y > 0; (6) D: all x-values except x =0, R: y > They are the same shape, but one is shifted up two units. 3x ; x 0.5 or a. 8 b. 1 c. 2 d. no solution 2x y=5x a. 9 b c = 2.6 d a. 15x 3 y b. y c. x 5 d. 8 x a. 2 b a. 4 x 4 b. 0 <x<3 c. 1<x 6 d. 5 x< Graphs (a) and (b) have a domain of <x<, while graphs (a) and (c) have a range of <y< a. x = ±4 b. ( 5, 17) c. x =4 or x = 2 d. x = See graph at right. Lesson ± or a. y= x 3+2 b. y= x a. D: the set of non-negative numbers; R: the set of non-negative numbers. b. D: x 2; R: y 3. c. The domain and range are each shifted along with the graph a. 3 b. 1 c x. (0, 0) and (4, 0), y. (0, 0), vertex. (2, 4) a. 12 b. 59 c. 7 d. 9 e. 13 f All equations are equivalent and have the same solution. x = a. 12x 2 +5x 2 b. 3m 2 +m 2 c. 5k 2 +26k a. x 12 b. 10<x<10 c. x <0 d. x < 5, x >1 Answer Key 81

5 Lesson a. x: ( 2, 0) and (5, 0), y: (0, 10) b. x: (1, 0), y: (0, 2) c. ( 3, 8) and (4, 6) d. They both represent a point at which two paths cross, but intercept specifically represents a curve crossing an axis, while intersect refers to any point where the graphs of two equations cross a. Intercept since the candle will stay lit until the weight is 0 grams b. Since we have two different growing patterns and we want to know when they charge the same amount, we are looking for an intersection. c. While it sounds like an intersection problem (two people are involved), the question asks for the amount of money when time = 0. Thus, we are looking for intercepts a. Equal Values Method, Substitution Method, and Elimination Method b. Using the Substitution Method, x 2 x 12=0, and x =4 or x = 3. The points are (4, 6) and ( 3, 8) The solutions are ( 1 2, 2) and ( 1, 1). The graph shows y= 1 with no roots x nor y-intercept and y=2x+1 with x-intercept ( 1, 0) and y-intercept (0,1) No solution; you cannot divide by zero Yes, they will intersect; top line. y= 1 4 x+10, bottom line. y= 1 3 x+3; they will cross at (12, 7) top line. x-intercept (40, 0) and y-intercept (0, 10); bottom line. x-intercept. ( 9, 0) and y-intercept (0, 3) Both (a) and (d) are equivalent. One way to test is to check that the solution to 4(3x 1)+3x =9x+5 makes the equation true (the solution is 3 2 ) The line should pass through ( 2, 5) and (0, 2); y= 3 2 x (a) and (b) are functions because each only has one output for each input a. D. <x<, R. 1 y 3 b. D. <x<, R. y 0 c. D. x 2, R. <y< All graphs have lines of symmetry. Graph (a) has multiple vertical lines of symmetry, one at each maximum and minimum; graph (b) has one line of symmetry at x =1 ; graph (c) has one line of symmetry at y=1. 82 Algebra Connections

6 Lesson Solutions vary. C is impossible a. one solution. (1, 1) b. no solutions c. two solutions. (1, 2) and (3, 2) d. one solution. ( 1, 0) e. no solution f. two solutions. (1, 4) and ( 2, 7) a. Using a standard window, it appears that there is only one point of intersection. b. There are actually two points. ( 4 3, 28 9 ) and (3 2, 3) a. 1 5 or 3 b. 1 2 or 3 c. 3 d. 7 or a. (3, 4) b. D: <x<, R. y He sold 9 watermelons (6, 20) and ( 1, 6) A B Lesson The only relation with no match is y= x a. D. 2 x 2, R. 4 y 4 b. D. <x<, R. y = 3 c. D. 0 x 4, R. 1 y 5 d. D. x > 0, R. all y-values except y= The graphs in parts (a) and (d) are not functions because they have two y-values for at least one x-value x 5 because the denominator cannot be y= 2 5 x ( 2, 10) a. 4x2 y 4 b. 18x 2 y c. xy 2 Answer Key 83

Department of Mathematics, University of Wisconsin-Madison Math 114 Worksheet Sections 3.1, 3.3, and 3.5

Department of Mathematics, University of Wisconsin-Madison Math 11 Worksheet Sections 3.1, 3.3, and 3.5 1. For f(x) = 5x + (a) Determine the slope and the y-intercept. f(x) = 5x + is of the form y = mx