What kind of transformation converts the graph of f(x) = 4|x + 1| - 3 into the graph of g(x) = 4|x + 9| - 3? Choices: (A)translation 8 units down (B)translation 8 units up (C)translation 8 units left (D)translation 8 units right

Identify Vertex of f(x): Identify the vertex of the function f(x) = 4|x + 1| - 3. The vertex of the absolute value function f(x) = 4|x + h| + k is (-h, k). For f(x) = 4|x + 1| - 3, h = -1 and k = -3. Vertex of f(x): (-1, -3)Identify Vertex of g(x): Identify the vertex of the function g(x) = 4|x + 9| - 3. Similarly, for g(x) = 4|x + h| + k, h = -9 and k = -3. Vertex of g(x): (-9, -3)Determine Transformation Type: Determine the type of transformation from f(x) to g(x). The change in the h-value from f(x) to g(x) is from -1 to -9, which is a shift of 8 units to the left. There is no change in the k-value, so there is no vertical shift. Transformation: translation 8 units left

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What kind of transformation converts the graph of $f(x) = 4|x + 1| - 3$ into the graph of $g(x) = 4|x + 9| - 3$ ? $\newline$ Choices: $\newline$ (A) translation $8$ units down $\newline$ (B) translation $8$ units up $\newline$ (C) translation $8$ units left $\newline$ (D) translation $8$ units right

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Algebra 2

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 4|x + 1| - 3

into the graph of

g(x) = 4|x + 9| - 3

\newline

Choices:

\newline

(A) translation

8

units down

\newline

(B) translation

8

units up

\newline

8

units left

\newline

(D) translation

8

units right

Identify Vertex of $f(x)$ : Identify the vertex of the function $f(x) = 4|x + 1| - 3$ . The vertex of the absolute value function $f(x) = 4|x + h| + k$ is $(-h, k)$ . For $f(x) = 4|x + 1| - 3$ , $h = -1$ and $k = -3$ . Vertex of $f(x)$ : $(-1, -3)$
Identify Vertex of $g(x)$ : Identify the vertex of the function $g(x) = 4|x + 9| - 3$ . Similarly, for $g(x) = 4|x + h| + k$ , $h = -9$ and $k = -3$ . Vertex of $g(x)$ : $(-9, -3)$
Determine Transformation Type: Determine the type of transformation from $f(x)$ to $g(x)$ . The change in the $h$ -value from $f(x)$ to $g(x)$ is from $-1$ to $-9$ , which is a shift of $8$ units to the left. There is no change in the $k$ -value, so there is no vertical shift. Transformation: translation $8$ units left