What kind of transformation converts the graph of f(x) = -9|x + 3| + 1 into the graph of g(x) = -9|x - 5| + 1? Choices: (A)translation 8 units down (B)translation 8 units up (C)translation 8 units right (D)translation 8 units left

Identify Vertex: Identify the vertex of the given function f(x). The vertex of the absolute value function f(x) = -9|x + 3| + 1 is at the point where the expression inside the absolute value is zero. Set x + 3 = 0 to find the x-coordinate of the vertex. x = -3 The y-coordinate is the value of f(x) when x = -3. f(-3) = -9|0| + 1 = 1 Vertex of f(x): (-3, 1)Find X-coordinate: Identify the vertex of the transformed function g(x). The vertex of the absolute value function g(x) = -9|x - 5| + 1 is at the point where the expression inside the absolute value is zero. Set x - 5 = 0 to find the x-coordinate of the vertex. x = 5 The y-coordinate is the value of g(x) when x = 5. g(5) = -9|0| + 1 = 1 Vertex of g(x): (5, 1)Determine Transformation Type: Determine the type of transformation. The vertices of f(x) and g(x) are (-3, 1) and (5, 1), respectively. Since the y-coordinates of the vertices are the same, there is no vertical transformation. The x-coordinates have changed, indicating a horizontal transformation.Determine Horizontal Shift: Determine the direction and magnitude of the horizontal transformation. To find the horizontal shift, calculate the difference between the x-coordinates of the vertices of f(x) and g(x). Shift = x-coordinate of g(x) - x-coordinate of f(x) Shift = 5 - (-3) Shift = 5 + 3 Shift = 8 Since the x-coordinate of the vertex of g(x) is greater than the x-coordinate of the vertex of f(x), the graph has shifted to the right.

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What kind of transformation converts the graph of $f(x) = -9|x + 3| + 1$ into the graph of $g(x) = -9|x - 5| + 1$ ? $\newline$ Choices: $\newline$ (A) translation $8$ units down $\newline$ (B) translation $8$ units up $\newline$ (C) translation $8$ units right $\newline$ (D) translation $8$ units left

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -9|x + 3| + 1

into the graph of

g(x) = -9|x - 5| + 1

\newline

Choices:

\newline

(A) translation

8

units down

\newline

(B) translation

8

units up

\newline

8

units right

\newline

(D) translation

8

units left

Identify Vertex: Identify the vertex of the given function $f(x)$ . The vertex of the absolute value function $f(x) = -9|x + 3| + 1$ is at the point where the expression inside the absolute value is zero. Set $x + 3 = 0$ to find the $x$ -coordinate of the vertex. $x = -3$ The $y$ -coordinate is the value of $f(x)$ when $x = -3$ . $f(-3) = -9|0| + 1 = 1$ Vertex of $f(x)$ : $f(x) = -9|x + 3| + 1$ $0$
Find X-coordinate: Identify the vertex of the transformed function $g(x)$ . The vertex of the absolute value function $g(x) = -9|x - 5| + 1$ is at the point where the expression inside the absolute value is zero. Set $x - 5 = 0$ to find the x-coordinate of the vertex. $x = 5$ The y-coordinate is the value of $g(x)$ when $x = 5$ . $g(5) = -9|0| + 1 = 1$ Vertex of $g(x)$ : $(5, 1)$
Determine Transformation Type: Determine the type of transformation. $\newline$ The vertices of $f(x)$ and $g(x)$ are $(-3, 1)$ and $(5, 1)$ , respectively. Since the $y$ -coordinates of the vertices are the same, there is no vertical transformation. The $x$ -coordinates have changed, indicating a horizontal transformation.
Determine Horizontal Shift: Determine the direction and magnitude of the horizontal transformation. $\newline$ To find the horizontal shift, calculate the difference between the x-coordinates of the vertices of $f(x)$ and $g(x)$ . $\newline$ Shift = x-coordinate of $g(x)$ - x-coordinate of $f(x)$ $\newline$ Shift = $5 - (-3)$ $\newline$ Shift = $5 + 3$ $\newline$ Shift = $8$ $\newline$ Since the x-coordinate of the vertex of $g(x)$ is greater than the x-coordinate of the vertex of $f(x)$ , the graph has shifted to the right.