Question

F(x)= 1/2 x^2+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

We are given the function
`f(x)= (1)/(2) x^2+4`.

The function f(x) is vertically stretched by a factor of 4.

Vertical stretch by factor 'k' changes the function f(x) to
`kf(x)`.

So, we get,

`g(x)=4f(x)`

`g(x)=4\huge \text((1)/(2) x^2+4\huge \text)`

`g(x)=2x^2 + 16`

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