What kind of transformation converts the graph of f(x) = -3|x + 8| - 2 into the graph of g(x) = -3|x + 8|? Choices: (A)translation 2 units up (B)translation 2 units right (C)translation 2 units down (D)translation 2 units left

Identify Structure: Identify the basic structure of the functions f(x) and g(x). Both functions have the same basic structure, which is a transformation of the absolute value function, scaled by a factor of -3 and shifted horizontally by 8 units to the left. The only difference between f(x) and g(x) is the vertical translation.Determine Shift: Determine the vertical shift between f(x) and g(x). The function f(x) = -3|x + 8| - 2 is shifted vertically down by 2 units compared to the function g(x) = -3|x + 8|, which has no vertical shift from the basic structure.Identify Transformation: Identify the type of transformation based on the vertical shift. Since f(x) is shifted down by 2 units to become g(x), the transformation is a translation 2 units up.Match Choices: Match the transformation to the given choices. The correct transformation is a translation 2 units up, which corresponds to choice (A).

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What kind of transformation converts the graph of $f(x) = -3|x + 8| - 2$ into the graph of $g(x) = -3|x + 8|$ ? $\newline$ Choices: $\newline$ (A) translation $2$ units up $\newline$ (B) translation $2$ units right $\newline$ (C) translation $2$ units down $\newline$ (D) translation $2$ units left

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Math Problems

Algebra 2

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -3|x + 8| - 2

into the graph of

g(x) = -3|x + 8|

\newline

Choices:

\newline

(A) translation

2

units up

\newline

(B) translation

2

units right

\newline

2

units down

\newline

(D) translation

2

units left

Identify Structure: Identify the basic structure of the functions $f(x)$ and $g(x)$ . Both functions have the same basic structure, which is a transformation of the absolute value function, scaled by a factor of $-3$ and shifted horizontally by $8$ units to the left. The only difference between $f(x)$ and $g(x)$ is the vertical translation.
Determine Shift: Determine the vertical shift between $f(x)$ and $g(x)$ . The function $f(x) = -3|x + 8| - 2$ is shifted vertically down by $2$ units compared to the function $g(x) = -3|x + 8|$ , which has no vertical shift from the basic structure.
Identify Transformation: Identify the type of transformation based on the vertical shift. Since $f(x)$ is shifted down by $2$ units to become $g(x)$ , the transformation is a translation $2$ units up.
Match Choices: Match the transformation to the given choices. $\newline$ The correct transformation is a translation $2$ units up, which corresponds to choice $(A)$ .