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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) =

Verified Answer :

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:

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

Step-by-step explanation:

We are given the function \(f(x)=\frac{1}{2}x^2+4\).

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,

\(g(x)=4f(x)\\\\g(x)=4(\frac{1}{2}x^2+4)\\\\g(x)=2x^2+16\)

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

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