Question

What value represents the horizontal translation from the graph of the parent function f(x) = x2 to the graph of the function g(x) = (x – 4)2 + 2?

Answer 1

Answer:

The value of horizontal shift is $-4$ that means graph of parent function is shifted to right by 4 units.

Step-by-step explanation:  

We have been given a parent function $f(x)=x^2$ and another function $g(x)=(x-4)^2+2$. We are asked to determine the horizontal translation from the graph of the parent function to the graph of the function g(x).

Let us recall translation rules.  

Horizontal translation:  

$f(x)\rightarrow f(x-a)=\text{Graph shifted to the right by 'a' units}$

$f(x)\rightarrow f(x+a)=\text{Graph shifted to the left by 'a' units}$

Vertical translation:

$f(x)\rightarrow f(x)-a=\text{Graph shifted downwards by 'a' units}$

$f(x)\rightarrow f(x)+a=\text{Graph shifted upwards by 'a' units}$

Upon looking at our both functions, we can see that parent function is shifted to right by 4 units and upwards by 2 units to get the the function g(x).

Therefore, the value of horizontal translation is $-4$, which indicates the graph is shifted to right by 4 units.

Answer 2

To move a function c units to the right, minus c from every x

we got

fro x^2 to (x-4)^2+2
4 was minused from every x
it was moved 4 units to the right