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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)

Respuesta :

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

For [tex]f(x)=2^x[/tex], and a=5
the vertically stretched function is then
[tex]g(x)=a f(x)=5*2^x[/tex]
SociometricStar

Answer:

[tex]f(x)=5(2^x)[/tex]

A is the correct option.

Step-by-step explanation:

We have been given the parent function [tex]f(x)=2^x[/tex]

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 [tex]f(x)=2^x[/tex] vertically stretched by a factor 5, hence, k = 5.

Therefore, the equation for the new function is

[tex]f(x)=5(2^x)[/tex]

A is the correct option.

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