Question

How are the graphs of the functions f(x) = StartRoot 16 EndRoot Superscript x and g(x) = RootIndex 3 StartRoot 64 EndRoot Superscript xrelated? The functions f(x) and g(x) are equivalent. The function g(x) increases at a faster rate. The function g(x) has a greater initial value. The function g(x) decreases at a faster rate.

Answer 1

Answer:

The function g(x) increases at a faster rate

The function g(x) has a greater initial value

Step-by-step explanation:

we have

$f(x)=(\sqrt{16})^{x}$

$g(x)=3(\sqrt{64})^{x}$

we know that

$16=4^{2}$

substitute in f(x)

$f(x)=(\sqrt{4^{2}})^{x}=4^x$

$64=8^{2}$

substitute in g(x)

$g(x)=3(\sqrt{8^{2}})^{x}=3(8)^x$

Compare the functions

f(x) and g(x) are not equivalent

Find the initial value

For x=0

$f(0)=4^0=1$

$g(0)=3(8)^0=3$

The initial value of g(x) is greater than the initial value of f(x)

using a graphing tool

The function g(x) increases at a faster rate than the function f(x) (see the attached figure)

That means ----> The value of g(x) is greater than the value of f(x) for the same value of x

therefore

The function g(x) increases at a faster rate

The function g(x) has a greater initial value

Answer 2

Answer:

The functions f(x) and g(x) are equivalent.

Step-by-step explanation:

option a