Question

Let f(x)=12x2+4. The function g(x) is a vertical stretch of f(x) by a factor of 4. What is the equation of g(x)?

Answer 1

A vertical stretch of function g(x)=S*f(x), where S is the scale factor.
We are given the scale factor=4, or S=4, so
g(x)=S*f(x)=4*f(x)=4(12x^2+4)=48x^2+16

Answer 2

The new function is
`g(x)=48x^2+16`

Explanation:

We are given,

The function
`f(x)=12x^2+4` is vertically stretched by a factor of 4.

Now, we know that,

Vertical stretch changes the function f(x) to
`kf(x)` where k is the scale factor.

So, we get,

The new function is
`g(x)=4f(x)`

i.e.
`g(x)=4(12x^2+4)`

i.e.
`g(x)=48x^2+16`

Thus, the equation of the new function is
`g(x)=48x^2+16`.