Use the image to answer the question.

Question

An parabola is drawn on a coordinate plane. Both axes range from negative 5 to 5 in one-unit increments.

Given the graph of the function f(x)
, complete the following table of the points for the horizontally reflected function f(−x)
.

(2 points)
x −1
−2
−3
f(−x)
Remaining Attempts : 3
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Answer 1

To find the values of the horizontally reflected function \( f(-x) \) based on \( f(x) \), we need to evaluate the function at the negative of the given \( x \) values.

Here are the steps you would take:

1. Identify \( f(x) \) values based on the points provided in the graph.
2. For each \( x \) value given in the table, calculate \( f(-x) \).

Let's say you have the following \( x \) values from the table:

• For \( x = -1 \), we need to find \( f(1) \).
• For \( x = -2 \), we need to find \( f(2) \).
• For \( x = -3 \), we need to find \( f(3) \).

Without the specific values from the graph, I can't provide exact answers for \( f(-x) \). However, once you have the values of \( f(1) \), \( f(2) \), and \( f(3) \) from your graph, you can fill in the table.

Make sure you read the graph values accurately and then just substitute:

• \( f(-1) \) will correspond to the value of \( f(1) \)
• \( f(-2) \) will correspond to the value of \( f(2) \)
• \( f(-3) \) will correspond to the value of \( f(3) \)

Once you have those values, you can fill out the table for \( f(-x) \).