B Apply

34. Think About a Plan Suppose you are playing with a yo-yo during a school talent show. The string is 3 ft long and you hold your hand 4 ft above the stage. The stage is 3.5 ft above the floor of the auditorium. Make a graph of the yo-yo's distance from the auditorium floor with respect to time during the show.
    • How could you graph the position of the yo-yo with respect to the stage, if you let time t = 0 t equals 0  when you start your routine?
    • How could you transform this graph to show the position with respect to the auditorium floor?
35. If someone started to take a video of your yo-yo routine when you were introduced, 10 seconds before you actually started, what transformation would you have to make to your graph to match their video?

Write the equations for f(x) and g(x). Then identify the reflection that transforms the graph of f(x) to the graph of g(x).

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39. Open-Ended Draw a figure in Quadrant I. Use a translation to move your figure into Quadrant III. Describe your translation.

40. Writing The graph of f(x) is shown below. Suppose each transformation of f(x) results in the given functions.

    

    1. vertical translation; g(x)
    2. reflection in the x-axis; h(x)
    3. vertical stretch; k(x),
    1. horizontal translation; m(x)
    2. Describe how the domain and range of the four new functions compare with the domain and range of f(x).
    3. Reasoning Do you think these effects on the domain and range of the original function hold true for all functions? Explain.

Graph each pair of functions on the same coordinate plane. Describe a transformation that changes f(x) to g(x).

41. f ( x ) = x + 1  ;  g ( x ) = x − 5 f open x close equals x plus 1 semicolon g open x close equals x minus 5
42. f ( x ) = − x + 3  ;  g ( x ) = x − 4 f open x close equals negative x plus 3 semicolon g open x close equals x minus 4
43. f ( x ) = x − 3  ;  g ( x ) = x + 1 f open x close equals x minus 3 semicolon g open x close equals x plus 1
44. f ( x ) = − x − 1  ;  g ( x ) = − x + 2 f open x close equals negative x minus 1 semicolon g open x close equals negative x plus 2

45. Error Analysis Your friend wrote the transformations shown to describe how to change the graph of f ( x ) = x 2 f open x close equals , x squared  to the graph of g ( x ) = 2 ( x + 1 ) 2 − 3 . g open x close equals 2 . open x plus 1 close squared . minus 3 .  Explain the error and give the correct transformations.

    

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