Question

The parabola that isngraphed has the points of (2,0), (1,-2), (3,-5). Given the graph of the function f(x), complete the table of points for the horizontally reflected fumction f(-x). The table is as follows: x:-1, -2, -3 f(-x):

Answer 1

Wrong

Answer 2

To find the values of the horizontally reflected function \( f(-x) \) based on the given points of the function \( f(x) \), we can use the following relationship:

If \( f(a) = b \), then \( f(-a) = b \) for any \( a \).

Given the points:

1. \( (2, 0) \) implies \( f(2) = 0 \) ⇒ \( f(-2) = 0 \)
2. \( (1, -2) \) implies \( f(1) = -2 \) ⇒ \( f(-1) = -2 \)
3. \( (3, -5) \) implies \( f(3) = -5 \) ⇒ \( f(-3) = -5 \)

Now, we can fill in the table for \( f(-x) \):

- For \( x = -1 \), \( f(-1) = -2 \)
- For \( x = -2 \), \( f(-2) = 0 \)
- For \( x = -3 \), \( f(-3) = -5 \)

So the completed table looks like this:

| x | f(-x) |
|----|-------|
| -1 | -2 |
| -2 | 0 |
| -3 | -5 |