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 parabola descends and then rises in quadrant 2. The curve passes through left parenthesis negative 3.6 comma 5 right parenthesis, left parenthesis negative 3 comma 2 right parenthesis, has a valley at left parenthesis negative 2 comma 0 right parenthesis, rises through left parenthesis negative 1 comma 2 right parenthesis, and left parenthesis negative 0.4 comma 5 right parenthesis. All values are approximate.

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

The correct table is:

x | g(x)
1 | −2
2 | 0
3 | −2

Reason: f has points (−1,2), (−2,0), (−3,2). Reflection about the origin sends (x,y) → (−x,−y), giving (1,−2), (2,0), (3,−2), so g(1)=−2, g(2)=0, g(3)=−2.