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 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
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 represent the function \( y = f(-x) \), we need to reflect the original function \( y = f(x) \) across the y-axis. This means that for every point \( (x, f(x)) \) on the original graph, there will be a corresponding point \( (-x, f(-x)) \) on the new graph.

Since I don't have the actual image of the parabola you mentioned, I can guide you in determining the correct table using generic points.

1. If, for example, you have a point on the original graph at \( (1, -2) \), it means that \( f(1) = -2 \). For \( f(-x) \), you reflect it across the y-axis, which would give you the point \( (-1, -2) \).

2. Similarly, if you have another point at \( (2, 0) \), then \( f(2) = 0 \) translates to \( f(-2) = 0 \), giving you the point \( (-2, 0) \).

3. Continue this process for each point provided in the original graph, and create new pairs as per the x-values being negated.

Out of the provided responses, select the table that applies the negation correctly based on the structure above. To correctly identify, you will need to check each provided table and see if the corresponding \( f(-x) \) values for \( x = -1, -2, -3, \ldots \) correctly match the intended outputs.

If you provide specific points from the parabola or describe its shape, I could be more precise in verifying the correct table.