Question

below is a graph of the gymnast's height, h, as a function of time, t 31 MacBook Pro 2 5 6 8 9 2 4 (e) Which of the following domains of h (r) allows h(t) to heve an inverse function? 0SIS48 19srs 5.8 version 4.24.147 MacBook Pro 嘸; G Search or type URL O. ground Section83 Copyof FINAL EXAM INAL EXAM 20 10

Answer 1

Answer:)

a.) The gymnast seems to attain a maximum height of m, as shown by the maximum y-value in the blue curve of h(t) v/s t.

31

b.) She lands on the trampoline when the height goes back to zero (she lands), which occurs at

5.8

c.) The height function can be inverted in the time-interval , and so that is a valid domain for h(t) to be inverted.

2.9 <t<5.8

d.) The story is to be changed as follows:

• At 2.9 seconds, the gymnast steps off the platform for the high wire, 31 m in the air.
• At 5.8 seconds she lands on a trampoline at ground level.

This makes sense, as the inverse function we chose gives us that t(31 m) = 2.9 s, and t(0 m) = 5.8 s.

e.) For the normal function, as time goes from 2.9 to 5.8s, the height decreases from 31m to 0m. Thus, for the inverse function, as height goes from 0m to 31m, the time goes from 5.8s to 2.9s. Hence the inverse function is a decreasing function. Hence, the correct option to choose would be $\boxed{(c.)}$