Answered

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What value represents the horizontal translation from the graph of the parent function [tex]f(x) = x^2[/tex] to the graph of the function [tex]g(x) = (x-4)^2 + 2[/tex]?

A. \(-4\)
B. \(-2\)
C. 2
D. 4

Sagot :

GinnyAnswer
To determine the horizontal translation from the parent function \( f(x) = x^2 \) to the function \( g(x) = (x-4)^2 + 2 \), we need to analyze the form of the function \( g(x) \).

The function \( g(x) \) can be written as:
[tex]\[ g(x) = (x-h)^2 + k \][/tex]
where \( h \) represents the horizontal shift and \( k \) represents the vertical shift.

In the given function \( g(x) = (x-4)^2 + 2 \):
- The expression inside the parentheses, \( x-4 \), indicates a horizontal shift.
- The number subtracted inside the parentheses (in this case, 4) tells us the direction and magnitude of the horizontal translation.

Specifically, \( x-4 \) means that every \( x \)-value of the parent function \( f(x) \) is shifted to the right by 4 units.

So, the value representing the horizontal translation is:
[tex]\[ 4 \][/tex]

Therefore, the correct answer is:
[tex]\[ 4 \][/tex]
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