Question

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)

Answer 1

Start with the points on f:
(-3.6, 5), (-3, 2), (-2, 0), (-1, 2), (-0.4, 5).

Reflection about the origin maps (x,y) -> (−x, −y). So the corresponding points on g(x) = −f(−x) are:
(3.6, −5), (3, −2), (2, 0), (1, −2), (0.4, −5).

Table:

Original f(x) | Reflected g(x)
-3.6 , 5 | 3.6 , −5
-3 , 2 | 3 , −2
-2 , 0 | 2 , 0
-1 , 2 | 1 , −2
-0.4 , 5 | 0.4 , −5

This table shows g(x)=−f(−x) is the reflection of f about the origin.