In the graph shown, suppose that f(x) = 3.5x and h(x) = 1.5x. Choose the statement that COULD be true. A) g(x)=5^x B) g(x)= 4^x C) g(x)= (.9)^x D) g(x)= \pi ^x

Question

In the graph shown, suppose that f(x) = 3.5x and h(x) = 1.5x. Choose the statement that COULD be true.

A)
`g(x)=5^x`
B)
`g(x)= 4^x`
C)
`g(x)= (.9)^x`
D)
`g(x)= \pi ^x`

Answer 1

Answer: D

Explanation:

The given functions are

Now these are exponential curves and the bases for the functions are 3.5 & 1.5

Also the graph of g(x) is between f(x) & h(x)

Hence the value of base called the scale factor must be between 3.5 & 1.5.

4 & 5 are more than 3.5

0.9 is smaller than 1.5

But π = 3.14 lies between 3.5 & 1.5.

Hence the only option which can represent the graph of g(x) is

Option D) is the right answer