Question

The functions f(x) and g(x) are shown on the graph.f(x)=x²What is g(x)?A. g(x)= -x^2-2B. g(x) = -x²+2C. g(x) = (-x)²-2D. g(x) = (-x)² + 2

Answer 1

Given the function:

`f(x)`

You can identify that its Vertex is at the Origin.

Look at the function:

`g(x)`

Notice that it was obtained by reflecting the first function across the x-axis and it also was shifted 2 units down.

According to the Transformation Rules for Functions:

1. If:

`-f(x)`

The function is reflected across the x-axis.

2. If:

`f(x)-k`

The function is shifted down "k" units.

You need to remember that the Parent Function (the simplest form) of Quadratic Equations is:

`y=x^2`

Therefore, the equation of the blue graph is:

`f(x)=x^2`

Therefore, you can write the following equation for the second function using the rules shown before:

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

Hence, the answer is: Option A.