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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?

2 Answers

3 votes
the -4  represents  a horizontal translation of 4 units to the right
User Grinnz
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4 votes

Answer:


-4 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 comparing our 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 horizontal translation is
-4, which indicates the graph is shifted to right by 4 units.

User Death
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