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

Identify Vertex: Identify the vertex of the function f(x) = -4|x - 2|. Since it's an absolute value function, the vertex is at x = 2. The y-value is f(2) = -4|2 - 2| = -4|0| = 0. Vertex of f(x): (2, 0)Identify Vertex: Identify the vertex of the function g(x) = -4|x - 2| - 6. The vertex is still at x = 2 since the absolute value expression didn't change. The y-value is g(2) = -4|2 - 2| - 6 = -4|0| - 6 = -6. Vertex of g(x): (2, -6)Determine Transformation: Determine the transformation from f(x) to g(x). The x-coordinate of the vertex didn't change, so there's no horizontal shift. The y-coordinate went from 0 to -6, which is a shift of 6 units down.

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

into the graph of

g(x) = -4|x - 2| - 6

\newline

Choices:

\newline

(A) translation

6

units down

\newline

(B) translation

6

units up

\newline

6

units left

\newline

(D) translation

6

units right

Identify Vertex: Identify the vertex of the function $f(x) = -4|x - 2|$ . $\newline$ Since it's an absolute value function, the vertex is at $x = 2$ . The y-value is $f(2) = -4|2 - 2| = -4|0| = 0$ . $\newline$ Vertex of $f(x)$ : $(2, 0)$
Identify Vertex: Identify the vertex of the function $g(x) = -4|x - 2| - 6$ . The vertex is still at $x = 2$ since the absolute value expression didn't change. The y-value is $g(2) = -4|2 - 2| - 6 = -4|0| - 6 = -6$ . Vertex of $g(x)$ : $(2, -6)$
Determine Transformation: Determine the transformation from $f(x)$ to $g(x)$ . The $x$ -coordinate of the vertex didn't change, so there's no horizontal shift. The $y$ -coordinate went from $0$ to $-6$ , which is a shift of $6$ units down.