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The parent function f(x)=x2 has been transformed to make the function g(x) by reflection f(x) over the x-axis , vertically shrinking by a factor of 1/2 and translating 2 units up. The equation for g(x) is expressed in which of the functions below

The parent function fxx2 has been transformed to make the function gx by reflection fx over the xaxis vertically shrinking by a factor of 12 and translating 2 u class=

Respuesta :

Given:

There are given that the parent function:

[tex]f(x)=x^2[/tex]

Explanation:

According to the concept:

The function reflected over the x-axis means, we need to multiply with a negative sign.

That means:

[tex]g(x)=-x^2[/tex]

And,

Vertically shrinking by a factor of 1/2 means, multiply by 1/2 in the entire function:

So,

[tex]g(x)=-\frac{1}{2}x^2[/tex]

Then,

Translating 2 units up means, adding 2 in the entire function:

So,

[tex]g(x)=-\frac{1}{2}x^2+2[/tex]

Final answer:

Hence, the correct option is C.

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