What kind of transformation converts the graph of f(x) = -8|x + 4| - 3 into the graph of g(x) = -8|x - 6| - 3? Choices: (A)translation 10 units right (B)translation 10 units left (C)translation 10 units up (D)translation 10 units down

Identify Vertex of f(x): Identify the vertex of the absolute value function f(x) = -8|x + 4| - 3. The vertex of f(x) occurs where the expression inside the absolute value is zero, so we set x + 4 = 0, which gives us x = -4. The y-coordinate of the vertex is the value of the function when x = -4, which is f(-4) = -8|0| - 3 = -3. Therefore, the vertex of f(x) is (-4, -3).Identify Vertex of g(x): Identify the vertex of the absolute value function g(x) = -8|x - 6| - 3. Similarly, the vertex of g(x) occurs where the expression inside the absolute value is zero, so we set x - 6 = 0, which gives us x = 6. The y-coordinate of the vertex is the value of the function when x = 6, which is g(6) = -8|0| - 3 = -3. Therefore, the vertex of g(x) is (6, -3).Determine Transformation: Determine the transformation from f(x) to g(x). The transformation from f(x) to g(x) involves a horizontal shift, since the y-coordinates of the vertices are the same (-3) and only the x-coordinates have changed. The shift is from x = -4 to x = 6, which is a shift to the right by 10 units.

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What kind of transformation converts the graph of $f(x) = -8|x + 4| - 3$ into the graph of $g(x) = -8|x - 6| - 3$ ? $\newline$ Choices: $\newline$ (A) translation $10$ units right $\newline$ (B) translation $10$ units left $\newline$ (C) translation $10$ units up $\newline$ (D) translation $10$ 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 + 4| - 3

into the graph of

g(x) = -8|x - 6| - 3

\newline

Choices:

\newline

(A) translation

10

units right

\newline

(B) translation

10

units left

\newline

10

units up

\newline

(D) translation

10

units down

Identify Vertex of $f(x)$ : Identify the vertex of the absolute value function $f(x) = -8|x + 4| - 3$ . The vertex of $f(x)$ occurs where the expression inside the absolute value is zero, so we set $x + 4 = 0$ , which gives us $x = -4$ . The $y$ -coordinate of the vertex is the value of the function when $x = -4$ , which is $f(-4) = -8|0| - 3 = -3$ . Therefore, the vertex of $f(x)$ is $(-4, -3)$ .
Identify Vertex of $g(x)$ : Identify the vertex of the absolute value function $g(x) = -8|x - 6| - 3$ . Similarly, the vertex of $g(x)$ occurs where the expression inside the absolute value is zero, so we set $x - 6 = 0$ , which gives us $x = 6$ . The $y$ -coordinate of the vertex is the value of the function when $x = 6$ , which is $g(6) = -8|0| - 3 = -3$ . Therefore, the vertex of $g(x)$ is $(6, -3)$ .
Determine Transformation: Determine the transformation from $f(x)$ to $g(x)$ . The transformation from $f(x)$ to $g(x)$ involves a horizontal shift, since the $y$ -coordinates of the vertices are the same $(-3)$ and only the $x$ -coordinates have changed. The shift is from $x = -4$ to $x = 6$ , which is a shift to the right by $10$ units.