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

Describe function transformations

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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

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.