What kind of transformation converts the graph of f(x) = 8|x - 2| - 2 into the graph of g(x) = 8|x + 4| - 2? Choices: (A)translation 6 units right (B)translation 6 units up (C)translation 6 units left (D)translation 6 units down

Identify Vertex of f(x): Let's identify the vertex of the absolute value function f(x) = 8|x - 2| - 2. The vertex of f(x) is at the point where the expression inside the absolute value is zero, which is x = 2. The y-coordinate of the vertex is the value of the function when x = 2, which is f(2) = 8|2 - 2| - 2 = 8|0| - 2 = 0 - 2 = -2. So the vertex of f(x) is (2, -2).Identify Vertex of g(x): Now let's identify the vertex of the absolute value function g(x) = 8|x + 4| - 2. The vertex of g(x) is at the point where the expression inside the absolute value is zero, which is x = -4. The y-coordinate of the vertex is the value of the function when x = -4, which is g(-4) = 8|-4 + 4| - 2 = 8|0| - 2 = 0 - 2 = -2. So the vertex of g(x) is (-4, -2).Determine Transformation: To determine the transformation, we compare the vertices of f(x) and g(x). The vertex of f(x) is (2, -2) and the vertex of g(x) is (-4, -2). The x-coordinate of the vertex has moved from 2 to -4, which is a shift of 6 units to the left. The y-coordinate has not changed, so there is no vertical shift.

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What kind of transformation converts the graph of $f(x) = 8|x - 2| - 2$ into the graph of $g(x) = 8|x + 4| - 2$ ? $\newline$ Choices: $\newline$ (A) translation $6$ units right $\newline$ (B) translation $6$ units up $\newline$ (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) = 8|x - 2| - 2

into the graph of

g(x) = 8|x + 4| - 2

\newline

Choices:

\newline

(A) translation

6

units right

\newline

(B) translation

6

units up

\newline

6

units left

\newline

(D) translation

6

units down

Identify Vertex of $f(x)$ : Let's identify the vertex of the absolute value function $f(x) = 8|x - 2| - 2$ . The vertex of $f(x)$ is at the point where the expression inside the absolute value is zero, which is $x = 2$ . The y-coordinate of the vertex is the value of the function when $x = 2$ , which is $f(2) = 8|2 - 2| - 2 = 8|0| - 2 = 0 - 2 = -2$ . So the vertex of $f(x)$ is $(2, -2)$ .
Identify Vertex of $g(x)$ : Now let's identify the vertex of the absolute value function $g(x) = 8|x + 4| - 2$ . The vertex of $g(x)$ is at the point where the expression inside the absolute value is zero, which is $x = -4$ . The y-coordinate of the vertex is the value of the function when $x = -4$ , which is $g(-4) = 8|-4 + 4| - 2 = 8|0| - 2 = 0 - 2 = -2$ . So the vertex of $g(x)$ is $(-4, -2)$ .
Determine Transformation: To determine the transformation, we compare the vertices of $f(x)$ and $g(x)$ . The vertex of $f(x)$ is $(2, -2)$ and the vertex of $g(x)$ is $(-4, -2)$ . The $x$ -coordinate of the vertex has moved from $2$ to $-4$ , which is a shift of $6$ units to the left. The $g(x)$ $0$ -coordinate has not changed, so there is no vertical shift.