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What kind of transformation converts the graph of $f(x) = |x - 4| - 1$ into the graph of $g(x) = |x - 6| - 1$ ? $\newline$ Choices: $\newline$ (A) translation $2$ units right $\newline$ (B) translation $2$ units left $\newline$ (C) translation $2$ units up $\newline$ (D) translation $2$ units down

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Describe function transformations

Full solution

Q. What kind of transformation converts the graph of

f(x) = |x - 4| - 1

into the graph of

g(x) = |x - 6| - 1

?

\newline

Choices:

\newline

(A) translation

2

units right

\newline

(B) translation

2

units left

\newline

(C) translation

2

units up

\newline

(D) translation

2

units down

Compare Functions: To determine the type of transformation, we need to compare the two functions $f(x)$ and $g(x)$ and see how the input ( $x$ ) and the output ( $y$ ) values are affected.
Original and Transformed Functions: The original function is $f(x) = |x - 4| - 1$ . The transformed function is $g(x) = |x - 6| - 1$ . We notice that the only change is in the expression inside the absolute value: from $(x - 4)$ to $(x - 6)$ .
Horizontal Shift: This change suggests a horizontal shift of the graph. Since the number inside the absolute value has increased from $4$ to $6$ , the graph has moved to the right.
Amount of Shift: The amount of the shift is equal to the difference in the numbers inside the absolute value, which is $6 - 4 = 2$ units.
Transformation Explanation: Therefore, the transformation is a translation $2$ units to the right.

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\newline

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