Complete the tables to show the parent function y=f(x)

Question

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 find the values of the translated function \( y = f(x + 5) \), we need to substitute \( x + 5 \) for \( x \) in the original function.

Given the original function values:

| \( x \) | \( y = f(x) \) | |---------|-----------------| | -2 | 5 | | -1 | 2 | | 0 | 1 | | 1 | 2 | | 2 | 5 |

To find \( y = f(x + 5) \), we need to determine the input \( x + 5 \) for each output \( y \).

To do this we can determine the required value of \( x \) for each \( y \):

1. For \( y = 5 \): Find \( x \) such that \( x + 5 = -2 \) or \( x + 5 = 2 \).

   • If \( x + 5 = -2 \), then \( x = -2 - 5 = -7 \).
   • If \( x + 5 = 2 \), then \( x = 2 - 5 = -3 \).
   • Therefore, both \( -7 \) and \( -3 \) can produce \( y = 5 \).

2. For \( y = 2 \): Find \( x \) such that \( x + 5 = -1 \) or \( x + 5 = 1 \).

   • If \( x + 5 = -1 \), then \( x = -1 - 5 = -6 \).
   • If \( x + 5 = 1 \), then \( x = 1 - 5 = -4 \).

3. For \( y = 1 \): Find \( x \) such that \( x + 5 = 0 \).

   • If \( x + 5 = 0 \), then \( x = 0 - 5 = -5 \).

4. For \( y = 2 \): Already calculated above.

5. For \( y = 5 \): Already calculated above.

Now we'll summarize these transformations into the table for the translated function \( y = f(x + 5) \).

Translated Function

| \( x \) | \( y = f(x + 5) \) | |---------|--------------------| | -7 | 5 | | -6 | 2 | | -5 | 1 | | -4 | 2 | | -3 | 5 |

Final Answer:

Original Function:

| \( x \) | \( y = f(x) \) | |---------|-----------------| | -2 | 5 | | -1 | 2 | | 0 | 1 | | 1 | 2 | | 2 | 5 |

Translated Function:

| \( x \) | \( y = f(x + 5) \) | |---------|--------------------| | -7 | 5 | | -6 | 2 | | -5 | 1 | | -4 | 2 | | -3 | 5 |