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diamong [38]
3 years ago
10

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)?

Mathematics
1 answer:
andrey2020 [161]3 years ago
6 0

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

Explanation:

Given that the function f(x) is f(x)=\frac{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)

<u>Equation of g(x):</u>

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(\frac{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

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