Question

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.

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

(1 point)
Responses

x f(−x)
1 2
2 0
3 2
x f left parenthesis negative x right parenthesis 1 2 2 0 3 2

x f(−x)
−1 −2
−2 0
−3 −2
x f left parenthesis negative x right parenthesis negative 1 negative 2 negative 2 0 negative 3 negative 2

x f(−x)
−1 2
−2 0
−3 2
x f left parenthesis negative x right parenthesis negative 1 2 negative 2 0 negative 3 2

x f(−x)
1 −2
2 0
3 −2
x f left parenthesis negative x right parenthesis 1 negative 2 2 0 3 negative 2
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Answer 1

To find the table that represents \( y = f(-x) \), we need to understand what this transformation does to the graph of the function. The transformation \( f(-x) \) takes the values of the function and reflects them across the y-axis.

This means when substituting \( -x \) into the function, the output of the function will be the same as the output for \( x \) but will have the input values inverted in sign.

To analyze the options:

1. For \( x = 1 \): check \( f(-1) \)
2. For \( x = 2 \): check \( f(-2) \)
3. For \( x = 3 \): check \( f(-3) \)

If the original function \( f(x) \) gives us values like \( f(1) \), \( f(2) \), and \( f(3) \), then \( f(-1) = f(1) \), \( f(-2) = f(2) \), and \( f(-3) = f(3) \).

If we have a function output table for \( y = f(x) \):

• \( f(1) = 2 \)
• \( f(2) = 0 \)
• \( f(3) = 2 \)

Then for \( f(-x) \):

• \( f(-1) = f(1) = 2 \)
• \( f(-2) = f(2) = 0 \)
• \( f(-3) = f(3) = 2 \)

Based on the reflection across the y-axis, we would find that \( f(-x) \) is:

• \( f(-1) = 2 \)
• \( f(-2) = 0 \)
• \( f(-3) = 2 \)

Thus, the correct table that represents \( y = f(-x) \) is:

x \( f(-x) \)
-1 2
-2 0
-3 2

Which corresponds to the third response option you listed:

• x \( f(-x) \)
  -1 2
  -2 0
  -3 2