Compare each of the functions shown below:
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Answer:
D. All three functions have the same rate of change.
Step-by-step explanation:
1. For the function f(x):
The rate of change is
[tex]\dfrac{f(\frac{3\pi}{2})-f(\pi)}{\frac{3\pi}{2}-\pi}=\dfrac{-4-0}{\frac{\pi}{2}}=-\dfrac{8}{\pi}.[/tex]
2. For the function g(x):
The rate of change is
[tex]\dfrac{g(\frac{3\pi}{2})-g(\pi)}{\frac{3\pi}{2}-\pi}=\dfrac{-4-0}{\frac{\pi}{2}}=-\dfrac{8}{\pi}.[/tex]
3. For the function h(x):
The rate of change is
[tex]\dfrac{h(\frac{3\pi}{2})-h(\pi)}{\frac{3\pi}{2}-\pi}=\dfrac{-2-2}{\frac{\pi}{2}}=-\dfrac{8}{\pi}.[/tex]
All three functions have the same rate of change.