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

Answer:

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

Step-by-step 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.