B Apply

31. Think About a Plan Graph y = − 2 | x + 3 | + 4 . y equals negative 2 vertical line x plus 3 vertical line plus 4 .  List the x- and y-intercepts, if any.
    • What is the vertex?
    • What does y equal at the x-intercept(s)? What does x equal at the y-intercept(s)?
32. Graph y = 4 | x − 3 | + 1 . y equals 4 vertical line x minus 3 vertical line plus 1 .  List the vertex and the x- and y-intercepts, if any.
33. Error Analysis A classmate says that the graphs of y = − 3 | x | y equals negative 3 vertical line x vertical line  and y = | − 3 x | y equals vertical line negative 3 x vertical line  are identical. Graph each function and explain why your classmate is not correct.
34. Graph each pair of equations on the same coordinate grid.
    1. y = 2|x + 1|; y = |2x + 1|
    2. y = 5 | x − 2 | ; y = | 5 x − 2 | y equals 5 vertical line x minus 2 vertical line semicolon y equals vertical line 5 x minus 2 vertical line
    3. Reasoning Explain why each pair of graphs in parts (a) and (b) are different.

35. The graphs of the absolute value functions f(x) and g(x) are given.

    
    Image Long Description

    1. Describe a series of transformations that you can use to transform f(x) into g(x).
    2. Reasoning If you change the order of the transformations you found in part(a), could you still transform f(x) into g(x)? Explain.

Graph each absolute value equation.

36. y = | − 1 4 x − 1 | y equals absolute value of . negative , 1 fourth , x minus 1 , end absolute value ,
37. y = | 5 2 x − 2 | y equals absolute value of . 5 halves , x minus 2 , end absolute value ,
38. y = | 3 2 x + 2 | y equals absolute value of . 3 halves , x plus 2 , end absolute value ,
39. y = | 3 x − 6 | + 1 y equals vertical line 3 x minus 6 vertical line plus 1
40. y = − | x − 3 | y equals negative vertical line x minus 3 vertical line
41. y = | 2 x + 6 | y equals vertical line 2 x plus 6 vertical line
42. y = 2 | x + 2 | − 3 y equals 2 vertical line x plus 2 vertical line negative 3
43. y = 6 − | 3 x | y equals 6 minus vertical line 3 x vertical line
44. y = 6 − | 3 x + 1 | y equals 6 minus vertical line 3 x plus 1 vertical line
45. 1. Graph the equations y = | 1 2 x − 6 | + 3 y equals vertical line , 1 half , x minus , 6 vertical line plus 3  and y = − | 1 2 x + 6 | − 3 y equals negative vertical line , 1 half , x plus 6 vertical line negative 3  on the same set of axes.
    2. Writing Describe the similarities and differences in the graphs.

C Challenge

Graph each absolute value equation.

46. y = | 3 x | − x 3 y equals vertical line 3 x vertical line negative , x over 3
47. y = 1 2 | x | + 4 | x − 1 | y equals , 1 half , vertical line x vertical line plus 4 vertical line x minus 1 vertical line
48. y = | 2 x | + | x − 4 | y equals vertical line 2 x vertical line plus vertical line x minus 4 vertical line

49. The graph below models the distance between a roadside stand and a car traveling at a constant speed. The x -axis represents time and the y -axis represents distance. Which equation best represents the relation shown in the graph?

    
    Image Long Description

    1. y = |60x|
    2. y = |40x|
    3. y = |x| + 60
    4. y = |x| + 40
50. 1. Open-Ended Find two absolute value equations with graphs that share a vertex.
    2. Find two absolute value equations with graphs that share part of a ray.

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