Question

Please help

If you vertically stretch the exponential function f(x)=2^x by a factor of 5, what is the equation of the new function
A.f(x)=5(2^x)
B.f(x)=10^x
C.f(x)=7^x
D.f(x)=2^(5x)

Answer 1

A vertical stretch of f(x) by a scale factor of a is
g(x)=a f(x)

For
`f(x)=2^x`, and a=5
the vertically stretched function is then

`g(x)=a f(x)=5*2^x`

Answer 2

`f(x)=5(2^x)`

A is the correct option.

Explanation:

We have been given the parent function
`f(x)=2^x`

We have the transformation rule:

Rule: If the parent function y =f(x) is stretched vertically by a factor 'k' then the equation becomes y=kf(x).

Here, the exponential function
`f(x)=2^x` vertically stretched by a factor 5, hence, k = 5.

Therefore, the equation for the new function is

`f(x)=5(2^x)`

A is the correct option.