Question

How would you shift the parent function y= x to graph the function y= (x-4)2 + 5?

A. The parent function would be shifted 4 units to the left and 5 units up.

B. The parent function would be shifted 4 units to the right and 5 units up.

C. The parent function would be shifted 5 units to the right and 4 units down.

D. The parent function would be shifted 5 units to the left and 4 units up.​

Answer 1

B. The parent function would be shifted 4 units to the right and 5 units up.

Explanation:

Given:

Parent function:

`y=x`

Transformed function:

`y=(x-4)+5`

To find the shifts made to the parent function.

Solution:

Translation Rules:

`f(x)\rightarrow f(x+c)`

If
`c>0` the function shifts
`c` units to the left.

If
`c<0` the function shifts
`c` units to the right.

`f(x)\rightarrow f(x)+c`

If
`c>0` the function shifts
`c` units to the up.

If
`c<0` the function shifts
`c` units to the down.

From the functions given the translation occurring can be given as:

`f(x)\rightarrow f(x-4)+5`

From the rules we can see that the parent function has moved 4 units to the right and 5 units up.