What kind of transformation converts the graph of f(x) = 10|x + 10| + 6 into the graph of g(x) = 10|x + 2| + 6? Choices: (A)translation 8 units down (B)translation 8 units up (C)translation 8 units right (D)translation 8 units left

Identify Vertex: Identify the vertex of the absolute value function f(x). The vertex of f(x) = 10|x + 10| + 6 is at the point where the expression inside the absolute value is zero. Set x + 10 = 0 to find the x-coordinate of the vertex. x = -10 The vertex of f(x) is at (-10, 6).Identify Vertex: Identify the vertex of the absolute value function g(x). The vertex of g(x) = 10|x + 2| + 6 is at the point where the expression inside the absolute value is zero. Set x + 2 = 0 to find the x-coordinate of the vertex. x = -2 The vertex of g(x) is at (-2, 6).Type of Transformation: Determine the type of transformation. The y-coordinates of the vertices of f(x) and g(x) are the same, so there is no vertical translation. The x-coordinate of the vertex of f(x) is -10, and the x-coordinate of the vertex of g(x) is -2. The transformation involves a horizontal shift.Calculate Shift: Calculate the horizontal shift. To find the horizontal shift, calculate the difference between the x-coordinates of the vertices of f(x) and g(x). Shift = x-coordinate of g(x) - x-coordinate of f(x) Shift = (-2) - (-10) Shift = -2 + 10 Shift = 8 The graph of f(x) is shifted 8 units to the right to become g(x).

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What kind of transformation converts the graph of $f(x) = 10|x + 10| + 6$ into the graph of $g(x) = 10|x + 2| + 6$ ? $\newline$ Choices: $\newline$ (A) translation $8$ units down $\newline$ (B) translation $8$ units up $\newline$ (C) translation $8$ units right $\newline$ (D) translation $8$ units left

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 10|x + 10| + 6

into the graph of

g(x) = 10|x + 2| + 6

\newline

Choices:

\newline

(A) translation

8

units down

\newline

(B) translation

8

units up

\newline

8

units right

\newline

(D) translation

8

units left

Identify Vertex: Identify the vertex of the absolute value function $f(x)$ . The vertex of $f(x) = 10|x + 10| + 6$ is at the point where the expression inside the absolute value is zero. Set $x + 10 = 0$ to find the $x$ -coordinate of the vertex. $x = -10$ The vertex of $f(x)$ is at $(-10, 6)$ .
Identify Vertex: Identify the vertex of the absolute value function $g(x)$ . The vertex of $g(x) = 10|x + 2| + 6$ is at the point where the expression inside the absolute value is zero. Set $x + 2 = 0$ to find the $x$ -coordinate of the vertex. $x = -2$ The vertex of $g(x)$ is at $(-2, 6)$ .
Type of Transformation: Determine the type of transformation. $\newline$ The $y$ -coordinates of the vertices of $f(x)$ and $g(x)$ are the same, so there is no vertical translation. $\newline$ The $x$ -coordinate of the vertex of $f(x)$ is $-10$ , and the $x$ -coordinate of the vertex of $g(x)$ is $-2$ . $\newline$ The transformation involves a horizontal shift.
Calculate Shift: Calculate the horizontal shift. $\newline$ To find the horizontal shift, calculate the difference between the x-coordinates of the vertices of $f(x)$ and $g(x)$ . $\newline$ Shift = x-coordinate of $g(x)$ - x-coordinate of $f(x)$ $\newline$ Shift = $(-2) - (-10)$ $\newline$ Shift = $-2 + 10$ $\newline$ Shift = $8$ $\newline$ The graph of $f(x)$ is shifted $8$ units to the right to become $g(x)$ .