Question

Let f(x)=1/2x2+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

The equation of g(x) is
`g(x)=2 x^(2)+16`

Step-by-step explanation:

Given that the function f(x) is
`f(x)=(1)/(2) x^(2)+4`

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,

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

Substituting the values,we have,

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

Simplifying the values, we get,

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

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