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.