What kind of transformation converts the graph of f(x) = -6|x - 4| + 1 into the graph of g(x) = -6|x - 4| + 8? Choices: (A)translation 7 units left (B)translation 7 units down (C)translation 7 units up (D)translation 7 units right

Identify Vertex f(x): Identify the vertex of the function f(x) = -6|x - 4| + 1. The vertex of the absolute value function f(x) = -6|x - 4| + 1 is at the point where the expression inside the absolute value is zero, which is at x = 4. The y-coordinate of the vertex is the constant term, which is +1. Therefore, the vertex of f(x) is (4, 1).Identify Vertex g(x): Identify the vertex of the function g(x) = -6|x - 4| + 8. Similarly, the vertex of the absolute value function g(x) = -6|x - 4| + 8 is at the point where the expression inside the absolute value is zero, which is at x = 4. The y-coordinate of the vertex is the constant term, which is +8. Therefore, the vertex of g(x) is (4, 8).Determine Transformation: Determine the transformation from f(x) to g(x). The transformation from f(x) to g(x) involves a change in the y-coordinate of the vertex from 1 to 8. This is a vertical shift. To find the amount of the shift, subtract the y-coordinate of the vertex of f(x) from the y-coordinate of the vertex of g(x): 8 - 1 = 7. This indicates a translation 7 units up.

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What kind of transformation converts the graph of $f(x) = -6|x - 4| + 1$ into the graph of $g(x) = -6|x - 4| + 8$ ? $\newline$ Choices: $\newline$ (A) translation $7$ units left $\newline$ (B) translation $7$ units down $\newline$ (C) translation $7$ units up $\newline$ (D) translation $7$ 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) = -6|x - 4| + 1

into the graph of

g(x) = -6|x - 4| + 8

\newline

Choices:

\newline

(A) translation

7

units left

\newline

(B) translation

7

units down

\newline

7

units up

\newline

(D) translation

7

units right

Identify Vertex $f(x)$ : Identify the vertex of the function $f(x) = -6|x - 4| + 1$ . The vertex of the absolute value function $f(x) = -6|x - 4| + 1$ is at the point where the expression inside the absolute value is zero, which is at $x = 4$ . The $y$ -coordinate of the vertex is the constant term, which is $+1$ . Therefore, the vertex of $f(x)$ is $(4, 1)$ .
Identify Vertex $g(x)$ : Identify the vertex of the function $g(x) = -6|x - 4| + 8$ . Similarly, the vertex of the absolute value function $g(x) = -6|x - 4| + 8$ is at the point where the expression inside the absolute value is zero, which is at $x = 4$ . The $y$ -coordinate of the vertex is the constant term, which is $+8$ . Therefore, the vertex of $g(x)$ is $(4, 8)$ .
Determine Transformation: Determine the transformation from $f(x)$ to $g(x)$ . The transformation from $f(x)$ to $g(x)$ involves a change in the $y$ -coordinate of the vertex from $1$ to $8$ . This is a vertical shift. To find the amount of the shift, subtract the $y$ -coordinate of the vertex of $f(x)$ from the $y$ -coordinate of the vertex of $g(x)$ : $g(x)$ $1$ . This indicates a translation $g(x)$ $2$ units up.