What kind of transformation converts the graph of f(x) = 4|x - 8| + 8 into the graph of g(x) = 4|x - 8| - 1? Choices: (A)translation 9 units down (B)translation 9 units up (C)translation 9 units right (D)translation 9 units left

Identify Vertex: Identify the vertex of the function f(x) = 4|x - 8| + 8. Vertex of f(x): (8, 8)Calculate Difference: Identify the vertex of the function g(x) = 4|x - 8| - 1. Vertex of g(x): (8, -1)Determine Transformation: Calculate the difference between the y-coordinates of the vertices of f(x) and g(x). Difference: 8 - (-1) = 9Determine the direction of the transformation based on the difference in y-coordinates. Since the y-coordinate of g(x) is 9 units less than the y-coordinate of f(x), the transformation is a translation 9 units down.

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What kind of transformation converts the graph of $f(x) = 4|x - 8| + 8$ into the graph of $g(x) = 4|x - 8| - 1$ ? $\newline$ Choices: $\newline$ (A) translation $9$ units down $\newline$ (B) translation $9$ units up $\newline$ (C) translation $9$ units right $\newline$ (D) translation $9$ 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) = 4|x - 8| + 8

into the graph of

g(x) = 4|x - 8| - 1

\newline

Choices:

\newline

(A) translation

9

units down

\newline

(B) translation

9

units up

\newline

9

units right

\newline

(D) translation

9

units left

Identify Vertex: Identify the vertex of the function $f(x) = 4|x - 8| + 8$ . $\newline$ Vertex of $f(x)$ : $(8, 8)$
Calculate Difference: Identify the vertex of the function $g(x) = 4|x - 8| - 1$ . $\newline$ Vertex of $g(x)$ : $(8, -1)$
Determine Transformation: Calculate the difference between the y-coordinates of the vertices of $f(x)$ and $g(x)$ . $\newline$ Difference: $8 - (-1) = 9$
Determine Transformation: Calculate the difference between the y-coordinates of the vertices of $f(x)$ and $g(x)$ . $\newline$ Difference: $8 - (-1) = 9$ Determine the direction of the transformation based on the difference in y-coordinates. $\newline$ Since the y-coordinate of $g(x)$ is $9$ units less than the y-coordinate of $f(x)$ , the transformation is a translation $9$ units down.