Question

Given the graph of the function f(x)
(0, 2)
𝑓
(
𝑥
)
, complete the following table of the points for the horizontally reflected function f(−x)
𝑓
(
−
𝑥
)
.

(2 points)
x −1
−
1
−2
−
2
−3
−
3
f(−x)
𝑓
(
−
𝑥
)

Answer 1

To find the values of the horizontally reflected function \( f(-x) \) for the given \( x \) values, we need to evaluate \( f(x) \) for the corresponding negative values of \( x \). This is because the reflection of the function across the y-axis means switching the signs of the \( x \) coordinates.

Here's how you can fill in the table based on the given \( x \) values:

| x | -1 | -2 | -3 |
|-------|--------|--------|--------|
| \( f(-x) \) | \( f(1) \) | \( f(2) \) | \( f(3) \) |

You need to know or look up the values of \( f(1) \), \( f(2) \), and \( f(3) \) from the graph or from the values provided for \( f(x) \).

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

For example, if you found that:
- \( f(1) = a \)
- \( f(2) = b \)
- \( f(3) = c \)

Then the table would look like:

| x | -1 | -2 | -3 |
|-------|--------|--------|--------|
| \( f(-x) \) | a | b | c |

Please provide the specific values of \( f(x) \) for \( x = 1, 2, 3 \) from the graph, and I can help you fill in the table accurately!