Question

Complete the tables to show the parent function y=f(x)
and its translation y=f(x+5)
. (2 points)
The table displays pairs of input-output for the original function.
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

Original:
x: -2 → y = 5
x: -1 → y = 2
x: 0 → y = 1
x: 1 → y = 2
x: 2 → y = 5

For y = f(x+5) we need x such that x+5 equals the original inputs. So x = original x − 5:

Translated:
x = -7 → y = f(-7+5)=f(-2)=5
x = -6 → y = f(-6+5)=f(-1)=2
x = -5 → y = f(-5+5)=f(0)=1
x = -4 → y = f(-4+5)=f(1)=2
x = -3 → y = f(-3+5)=f(2)=5