Use the image to answer the question.

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 1 negative 2 2 0 3 negative 2

x f(−x)
−1 2
−2 0
−3 2

Answer 1

To find the table that represents \( y = f(-x) \), we need to reflect the original function \( y = f(x) \) across the y-axis. This means that for every positive x-value in the original function, we will find the corresponding value at the negative of that x-value in the new function.

Let's assume the original function \( f(x) \) has the following points based on the descriptions:

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

For \( f(-x) \), we look for:

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

Based on this logic, the corresponding values for \( y = f(-x) \) would be:

• When \( x = -1 \), \( f(-(-1)) = f(1) = 2 \)
• When \( x = -2 \), \( f(-(-2)) = f(2) = 0 \)
• When \( x = -3 \), \( f(-(-3)) = f(3) = 2 \)

Now, let's evaluate the provided options:

• The correct table for \( y = f(-x) \) should show:
  • \( x = -1 \), \( f(-x) = 2 \)
  • \( x = -2 \), \( f(-x) = 0 \)
  • \( x = -3 \), \( f(-x) = 2 \)

Based on this evaluation, the correct response is:

x f(−x) -1 2 -2 0 -3 2

So, the correct answer is:

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