What kind of transformation converts the graph of f(x) = 9|x - 2| - 2 into the graph of g(x) = 9|x + 1| - 2? Choices: (A)translation 3 units left (B)translation 3 units up (C)translation 3 units right (D)translation 3 units down

Identify Vertex of f(x): Identify the vertex of the function f(x) = 9|x - 2| - 2. The vertex of the absolute value function f(x) = 9|x - h| - k is at the point (h, k). For f(x) = 9|x - 2| - 2, h = 2 and k = -2. Vertex of f(x): (2, -2)Identify Vertex of g(x): Identify the vertex of the function g(x) = 9|x + 1| - 2. Similarly, for g(x) = 9|x - h| - k, h = -1 and k = -2. Vertex of g(x): (-1, -2)Determine Horizontal Shift: Determine the horizontal shift between the vertices of f(x) and g(x). The horizontal shift is the difference in the x-coordinates of the vertices. The vertex of f(x) is at (2, -2) and the vertex of g(x) is at (-1, -2). Horizontal shift: 2 - (-1) = 3 units to the left.Determine Vertical Shift: Determine the vertical shift between the vertices of f(x) and g(x). The vertical shift is the difference in the y-coordinates of the vertices. Since both y-coordinates are -2, there is no vertical shift. Vertical shift: -2 - (-2) = 0 units.

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What kind of transformation converts the graph of $f(x) = 9|x - 2| - 2$ into the graph of $g(x) = 9|x + 1| - 2$ ? $\newline$ Choices: $\newline$ (A) translation $3$ units left $\newline$ (B) translation $3$ units up $\newline$ (C) translation $3$ units right $\newline$ (D) translation $3$ units down

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Algebra 2

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 9|x - 2| - 2

into the graph of

g(x) = 9|x + 1| - 2

\newline

Choices:

\newline

(A) translation

3

units left

\newline

(B) translation

3

units up

\newline

3

units right

\newline

(D) translation

3

units down

Identify Vertex of $f(x)$ : Identify the vertex of the function $f(x) = 9|x - 2| - 2$ . The vertex of the absolute value function $f(x) = 9|x - h| - k$ is at the point $(h, k)$ . For $f(x) = 9|x - 2| - 2$ , $h = 2$ and $k = -2$ . Vertex of $f(x)$ : $(2, -2)$
Identify Vertex of $g(x)$ : Identify the vertex of the function $g(x) = 9|x + 1| - 2$ . Similarly, for $g(x) = 9|x - h| - k$ , $h = -1$ and $k = -2$ . Vertex of $g(x)$ : $(-1, -2)$
Determine Horizontal Shift: Determine the horizontal shift between the vertices of $f(x)$ and $g(x)$ . The horizontal shift is the difference in the $x$ -coordinates of the vertices. The vertex of $f(x)$ is at $(2, -2)$ and the vertex of $g(x)$ is at $(-1, -2)$ . Horizontal shift: $2 - (-1) = 3$ units to the left.
Determine Vertical Shift: Determine the vertical shift between the vertices of $f(x)$ and $g(x)$ . The vertical shift is the difference in the $y$ -coordinates of the vertices. Since both $y$ -coordinates are $-2$ , there is no vertical shift. Vertical shift: $-2 - (-2) = 0$ units.