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 original graph of the function y=f(x)
is shown. Select the table that represents y=f(−x)
.

(1 point)

This table shows the relationship between x and the function f(-x).
x f(−x)

−1
−2

−2
0
−3
−2


This table shows the relationship between x and the function f(-x).
x f(−x)

−1
2
−2
0
−3
2

This table shows the relationship between x and the function f(-x).
x f(−x)

1 2
2 0
3 2

This table shows the relationship between x and the function f(-x).
x f(−x)

1 −2

2 0
3 −2

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Answer 1

The correct table is the third one: x = 1 → 2, 2 → 0, 3 → 2.

Reason: f(−x) at x = a equals f(a with sign reversed). So for x = 1,2,3 look at the original graph at x = −1,−2,−3, which have y-values 2, 0, 2 respectively.