f(x)=3/4x^2 −1.
A vertical stretch by a factor of 8 you multiply the number with x by the factor:
3/4 x 8 = 6
g(x) = 6x^2-1
The function g(x) is a vertical stretch of f(x) by a factor of 8, the equation of function g(x) is 6[tex]x^{2}[/tex] - 1.
The vertical stretch of a function by a factor is meant by expanding the function by the given factor. To find the vertical stretch, we multiply the dependent variable parameter by the given factor.
Given function f(x) = [tex]\frac{3}{4}x^{2} - 1[/tex] .
Also given that The function g(x) is a vertical stretch of f(x) by a factor of 8.
Thus we have to multiply the parameter [tex]x^{2}[/tex] by 8 ,
Replacing the variable [tex]x^{2}[/tex] by 8[tex]x^{2}[/tex] .
⇒ g(x) = [tex]\frac{3}{4}*8x^{2} - 1[/tex]
∴ g(x) = 6[tex]x^{2}[/tex] - 1
Therefore, the function g(x) is a vertical stretch of f(x) by a factor of 8, the equation of function g(x) is 6[tex]x^{2}[/tex] - 1.
To learn more vertical stretch, refer -
https://brainly.com/question/11380655
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