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

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Answer 1

Reflection about the origin sends (x,y) -> (−x,−y). From f(x)=2(x+2)^2 the graph has points (-3,2), (-2,0), (-1,2). Reflecting gives (3,-2), (2,0), (1,-2). So the correct table is:

x g(x)
1 -2
2 0
3 -2