Question

Let f(x)=1/2x^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)?



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g(x) =

Answer 1

Answer: g(x) = 1/2x^2+8

The original +4 is along the y-axis (y-intercept) so you add the 4 onto it since the y-axis is vertically calculated, unlike x that is a horizontal line.

Answer 2

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

Explanation:

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((1)/(2)x^2+4)\\\\g(x)=2x^2+16`

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