Question

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

Answer 1

Given:

There are given that the parent function:

`f(x)=x^2`

Step-by-step explanation:

According to the concept:

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

That means:

`g(x)=-x^2`

And,

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

So,

`g(x)=-(1)/(2)x^2`

Then,

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

So,

`g(x)=-(1)/(2)x^2+2`

Final answer:

Hence, the correct option is C.