What kind of transformation converts the graph of f(x) = |x - 4| - 3 into the graph of g(x) = |x + 2| - 3? Choices: (A)translation 6 units up (B)translation 6 units right (C)translation 6 units left (D)translation 6 units down

Identify Vertex f(x): Identify the vertex of the function f(x) = |x - 4| - 3. The vertex of the absolute value function f(x) = |x - h| + k is (h, k). For f(x) = |x - 4| - 3, h = 4 and k = -3. Vertex of f(x): (4, -3)Identify Vertex g(x): Identify the vertex of the function g(x) = |x + 2| - 3. Similarly, for g(x) = |x + 2| - 3, h = -2 and k = -3. Vertex of g(x): (-2, -3)Determine Horizontal Shift: Determine the horizontal shift between the vertices of f(x) and g(x). The shift in the x-coordinate from the vertex of f(x) to the vertex of g(x) is from 4 to -2, which is a shift of 6 units to the left. Shift: 6 units left

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What kind of transformation converts the graph of $f(x) = |x - 4| - 3$ into the graph of $g(x) = |x + 2| - 3$ ? $\newline$ Choices: $\newline$ (A) translation $6$ units up $\newline$ (B) translation $6$ units right $\newline$ (C) translation $6$ units left $\newline$ (D) translation $6$ 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) = |x - 4| - 3

into the graph of

g(x) = |x + 2| - 3

\newline

Choices:

\newline

(A) translation

6

units up

\newline

(B) translation

6

units right

\newline

6

units left

\newline

(D) translation

6

units down

Identify Vertex $f(x)$ : Identify the vertex of the function $f(x) = |x - 4| - 3$ . The vertex of the absolute value function $f(x) = |x - h| + k$ is $(h, k)$ . For $f(x) = |x - 4| - 3$ , $h = 4$ and $k = -3$ . Vertex of $f(x)$ : $(4, -3)$
Identify Vertex $g(x)$ : Identify the vertex of the function $g(x) = |x + 2| - 3$ . Similarly, for $g(x) = |x + 2| - 3$ , $h = -2$ and $k = -3$ . Vertex of $g(x)$ : $(-2, -3)$
Determine Horizontal Shift: Determine the horizontal shift between the vertices of $f(x)$ and $g(x)$ . The shift in the $x$ -coordinate from the vertex of $f(x)$ to the vertex of $g(x)$ is from $4$ to $-2$ , which is a shift of $6$ units to the left. Shift: $6$ units left