The equation of g(x) is [tex]g(x)=2 x^{2}+16[/tex]
Explanation:
Given that the function f(x) is [tex]f(x)=\frac{1}{2} x^{2}+4[/tex]
Also, given that the function g(x) is a vertical stretch of f(x) by a factor of 4.
We need to determine the equation of g(x)
Equation of g(x):
The vertical stretch of the function can be determined by multiplying the factor 4 with the function f(x).
Thus, we have,
[tex]g(x)=4 f(x)[/tex]
Substituting the values,we have,
[tex]g(x)=4\left(\frac{1}{2} x^{2}+4\right)[/tex]
Simplifying the values, we get,
[tex]g(x)=2 x^{2}+16[/tex]
Hence, the equation of g(x) is [tex]g(x)=2 x^{2}+16[/tex]
