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 2 negative 2 0 negative 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

Answer 1

To find the values for \( y = f(-x) \) based on the graph of \( y = f(x) \), we need to reflect the values of \( f(x) \) across the y-axis.

This means that for every \( x \) value in the function \( f(x) \), we retrieve the corresponding \( y \) value from \( f(x) \), but for \( -x \), we take the \( y \) value from \( f(x) \) at \( x \).

Let's say we have found the values \( f(x) \) for specific \( x \):
- For \( x = 1 \), \( f(1) = y_1 \)
- For \( x = 2 \), \( f(2) = y_2 \)
- For \( x = 3 \), \( f(3) = y_3 \)

To find \( f(-x) \):
- For \( -1 \), \( f(-1) = f(1) \)
- For \( -2 \), \( f(-2) = f(2) \)
- For \( -3 \), \( f(-3) = f(3) \)

Now we can map out potential responses based on the values of \( f(x) \).

1. Inspect the first option:
- \( f(-1) = 2 \)
- \( f(-2) = 0 \)
- \( f(-3) = 2 \)

2. For the second option:
- \( f(-1) = 2 \)
- \( f(-2) = 0 \)
- \( f(-3) = 2 \)

3. For the third option:
- For negatives, these seem incorrect.

4. Last option (checking):
- \( f(-1) = -2 \)
- \( f(-2) = 0 \)
- \( f(-3) = -2 \)

Based on the reflection rule, the values derived should correspond to those seen at their positive \( x \) partners.

Given our context in analysis, the values that appear valid from the likely direct reflection from f(x) aligns with:

- First choice containing outputs \( 2, 0, 2 \) for respective inputs at \( -1, -2, -3 \).

So we'll select this correctly reflected table correspondingly that matches the transformation of negative values to original points in function by extrapolating from positive ones.

The best response would be:

**x f(−x)**
-1 2
-2 0
-3 2