What kind of transformation converts the graph of f(x) = 4|x - 5| + 9 into the graph of g(x) = 4|x - 6| + 9? Choices: (A)translation 1 unit up (B)translation 1 unit down (C)translation 1 unit right (D)translation 1 unit left

Analyze Functions: Analyze the given functions f(x) = 4|x - 5| + 9 and g(x) = 4|x - 6| + 9 to determine the type of transformation. The functions are in the form of y = a|x - h| + k, where (h, k) is the vertex of the graph of the function. For f(x), the vertex is at (5, 9). For g(x), the vertex is at (6, 9).Compare Vertices: Compare the vertices of f(x) and g(x) to determine the direction of the transformation. The vertex of f(x) is (5, 9) and the vertex of g(x) is (6, 9). The y-coordinate has not changed, so there is no vertical translation. The x-coordinate has increased from 5 to 6, indicating a horizontal translation to the right.Calculate Translation Magnitude: Calculate the magnitude of the horizontal translation. The change in the x-coordinate from the vertex of f(x) to the vertex of g(x) is 6 - 5 = 1. This means the graph of f(x) has been translated 1 unit to the right to obtain the graph of g(x).

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What kind of transformation converts the graph of $f(x) = 4|x - 5| + 9$ into the graph of $g(x) = 4|x - 6| + 9$ ? $\newline$ Choices: $\newline$ (A) translation $1$ unit up $\newline$ (B) translation $1$ unit down $\newline$ (C) translation $1$ unit right $\newline$ (D) translation $1$ unit left

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Math Problems

Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 4|x - 5| + 9

into the graph of

g(x) = 4|x - 6| + 9

\newline

Choices:

\newline

(A) translation

1

unit up

\newline

(B) translation

1

unit down

\newline

1

unit right

\newline

(D) translation

1

unit left

Analyze Functions: Analyze the given functions $f(x) = 4|x - 5| + 9$ and $g(x) = 4|x - 6| + 9$ to determine the type of transformation. $\newline$ The functions are in the form of $y = a|x - h| + k$ , where $(h, k)$ is the vertex of the graph of the function. $\newline$ For $f(x)$ , the vertex is at $(5, 9)$ . $\newline$ For $g(x)$ , the vertex is at $(6, 9)$ .
Compare Vertices: Compare the vertices of $f(x)$ and $g(x)$ to determine the direction of the transformation. $\newline$ The vertex of $f(x)$ is $(5, 9)$ and the vertex of $g(x)$ is $(6, 9)$ . $\newline$ The $y$ -coordinate has not changed, so there is no vertical translation. $\newline$ The $x$ -coordinate has increased from $5$ to $6$ , indicating a horizontal translation to the right.
Calculate Translation Magnitude: Calculate the magnitude of the horizontal translation. $\newline$ The change in the $x$ -coordinate from the vertex of $f(x)$ to the vertex of $g(x)$ is $6 - 5 = 1$ . $\newline$ This means the graph of $f(x)$ has been translated $1$ unit to the right to obtain the graph of $g(x)$ .