Question

Use the image to answer the question.

A parabola is drawn on a coordinate plane. Both axes range from negative 5 to 5 in one-unit increments.
▶Click for Long Desc

The function f(x)=2(x+2)2
is shown in the graph. Which table shows that g(x)=−f(−x)
results in a reflection about the origin of the function graphed?

Hint: Make a table of the x
- and y
-coordinates based on the graph. Use these points to determine the coordinates of the function reflected about the origin.

(1 point)

x g(x)

−1
2
−2
0
−3
2

x g(x)

−1
−2

−2
0
−3
−2


x g(x)

1 2
2 0
3 2

x g(x)

1 −2

2 0
3 −2

Answer 1

g(x) = −f(−x) = −2(x−2)^2, so using f(−3)=2, f(−2)=0, f(−1)=2 gives
g(3)=−f(−3)=−2, g(2)=0, g(1)=−2.

So the correct table is the last one:
x: 1 → −2, 2 → 0, 3 → −2.