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 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
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

Answer 1

To find the values of \( y = f(-x) \) based on the original graph of \( y = f(x) \), we need to reflect the points of the graph across the y-axis. This means that for every \( x \) value, we will take the corresponding \( f(x) \) value and switch the sign of \( x \), effectively finding \( f(-x) \).

Without the actual image of the graph, I must describe the general approach:

1. Identify key points on the graph of \( y = f(x) \).
2. For each point \( (x, y) \) on that graph, find the point \( (-x, y) \) for the graph of \( y = f(-x) \).
3. Organize these points into a table format.

Given the options you've provided, we would need to match the reflected points to the given tables.

Here’s a breakdown of the provided tables, looking for potential reflections:

1. **First table**:
- \( x: -1 \rightarrow 2 \)
- The \( y \) value is different; continue checking.

2. **Second table**:
- \( x: 1 \rightarrow -2 \)
- Matches if the original \( f(1) = -2 \).

3. **Third table**:
- \( x: -1 \rightarrow 2 \) (there’s a non-matching \( y \) here as well).

4. **Fourth table**:
- \( x: 1 \rightarrow 2 \)
- Again, it seems to ignore the negative reflection.

To choose the table that represents \( y = f(-x) \), look at the combinations of \( (x, f(-x)) \) ensuring to reflect each point accurately from \( y = f(x) \) to \( f(-x) \).

If matching the reflected values of the original graph supports the second table, where all points reflect correctly, that would be the right choice.

Without the actual graph, I suggest evaluating the points one by one with the reflection principle above to finalize your choice. If you can share the actual graph being referenced, I could give a more specific response based on identified transformations.