Question

Complete the tables to show the parent function y=f(x)
and its translation y=f(x+5)
. (2 points)
Original Function
x
y=f(x)
−2
5
−1
2
0 1
1 2
2 5

Translated Function
x
y=f(x+5)
5
2
1
2
5

Answer 1

To complete the table for the translated function \( y = f(x + 5) \), we need to find the corresponding \( y \) values for each of the translated \( x \) values in the original function.

The translation \( x + 5 \) means we take each \( x \) value in the original function and subtract 5 to get the corresponding original \( x \) value needed to find \( y \):

1. For \( x = -2 \):
\[
y = f(-2 + 5) = f(3) \rightarrow \text{(not given, so we can't compute the value)}
\]

2. For \( x = -1 \):
\[
y = f(-1 + 5) = f(4) \rightarrow \text{(not given, so we can't compute the value)}
\]

3. For \( x = 0 \):
\[
y = f(0 + 5) = f(5) \rightarrow 5
\]

4. For \( x = 1 \):
\[
y = f(1 + 5) = f(6) \rightarrow \text{(not given, so we can't compute the value)}
\]

5. For \( x = 2 \):
\[
y = f(2 + 5) = f(7) \rightarrow \text{(not given, so we can't compute the value)}
\]

Since we don't have values for \( f(3) \), \( f(4) \), \( f(6) \), or \( f(7) \), we can only fill in the known value for \( x = 5 \):

For \( x = 5 \):
\[
y = f(5 + 5) = f(10) \rightarrow \text{(not given, so we can't compute the value)}
\]

Given what we have, let's summarize the tables:

### Original Function
| x | y = f(x) |
|----|----------|
| -2 | 5 |
| -1 | 2 |
| 0 | 1 |
| 1 | 2 |
| 2 | 5 |

### Translated Function
| x | y = f(x + 5) |
|----|------------|
| -2 | (not given) |
| -1 | (not given) |
| 0 | 5 |
| 1 | (not given) |
| 2 | (not given) |
| 5 | (not given) |

Please provide the corresponding values for the function at \( f(3) \), \( f(4) \), \( f(6) \), and \( f(7) \) if available, so the table can be completed.