B Apply

37. Think About a Plan The time t in seconds for a pendulum to complete one full cycle is given by the function t = 1.11 l , t equals , 1.11 , square root of l comma  where l is the length of the pendulum in feet. How long is a pendulum that takes 4.5 seconds to complete one full cycle? 6 seconds to complete one full cycle? Round your answers to the nearest hundredth.
    • How can you use a graph to approximate the length of a pendulum?
    • How can you check your answers algebraically?

Graph each function. Find the domain and range.

38. y = 4 x − 2 3 + 1 y equals 4 . cube root of x minus 2 end root , . plus 1
39. y = 1 2 x − 1 + 3 y equals , 1 half . square root of x minus 1 end root , plus 3
40. y = 3 x − 6 3 + 2 y equals 3 . cube root of x minus 6 end root , . plus 2

41. Suppose that a function pairs elements from set A with elements from set B. Recall that a function is called onto if every element in B is paired with at least one element in A.

    

    1. The graph shows a transformation of y = x . y equals square root of x .  Write the function.
    2. What are the domain and range of the function?
    3. For the domain, is the function onto the set of nonnegative real numbers? Explain.
42. Open-Ended Write a radical function such that for its domain, the function is onto the set of real numbers such that y ≤ 3 . y less than or equal to 3 .

Rewrite each function to make it easy to graph using transformations of its parent function. Describe the graph.

43. y = 25 x − 100 − 1 y equals . square root of 25 x minus 100 end root . minus 1
44. y = 36 x + 108 + 4 y equals . square root of 36 x plus 108 end root . plus 4
45. y = − 8 x − 2 3 y equals negative . cube root of 8 x minus 2 end root ,
46. y = x − 1 4 − 2 y equals . square root of fraction x minus 1 , over 4 end fraction end root . minus 2
47. y = 10 − x + 3 27 3 y equals 10 minus . cube root of fraction x plus 3 , over 27 end fraction end root ,
48. y = x 9 + 1 + 5 y equals . square root of x over 9 , plus 1 plus 5 end root

Graphing Calculator Solve the following radical equations.

49. 2 x = ( x + 1 ) 2 square root of x equals . square root of open , x plus 1 , close end root
50. ( x + 3 ) = 4 ( x ) − 2 square root of open , x plus 3 , close end root . equals 4 , square root of open x close end root , minus 2
51. x − 1 3 = x − 1 cube root of x minus 1 end root , . equals square root of x minus 1
52. 1. Solve 3 − ( x − 3 ) = x 3 minus . square root of open , x minus 3 , close end root . equals x  algebraically.
    2. Solve the equation from part (a) graphically.
    3. What do you notice about your answer to part (a) compared to your answer to part (b)?
53. Electronics The size of a computer monitor is given as the length of the screen's diagonal d in inches. The equation d = 5 6 3 A d equals , 5 sixths , square root of 3 eh end root  models the length of a diagonal of a monitor screen with area A in square inches.
    1. Graph the equation on your calculator.
    2. Suppose you want to buy a new monitor with a screen that is twice the area of your old screen. Your old screen has a diagonal of 15 inches. What will be the diagonal of your new screen?
54. Physics You can model time t, in seconds, an object takes to reach the ground falling from height H, in meters, by t ( H ) = 2 H g . t , open h close , equals , square root of fraction 2 h , over g end fraction end root , .  The value of g is 9 . 81  m/s 2 . 9 . 81 , mslashs squared . . If an object takes 7 seconds to fall to the ground, what was its initial height?

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