What kind of transformation converts the graph of f(x) = -4|x - 7| + 3 into the graph of g(x) = -4|x - 7| - 1? Choices: (A)translation 4 units left (B)translation 4 units up (C)translation 4 units right (D)translation 4 units down

Identify Vertex of f(x): Identify the vertex of the function f(x) = -4|x - 7| + 3. The vertex of the absolute value function f(x) = -4|x - 7| + 3 is at the point where x - 7 = 0, which is x = 7. The y-coordinate of the vertex is the constant term, which is +3. Therefore, the vertex of f(x) is at (7, 3).Identify Vertex of g(x): Identify the vertex of the function g(x) = -4|x - 7| - 1. Similarly, the vertex of the absolute value function g(x) = -4|x - 7| - 1 is at the point where x - 7 = 0, which is x = 7. The y-coordinate of the vertex is the constant term, which is -1. Therefore, the vertex of g(x) is at (7, -1).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 +3 to -1. This is a vertical shift. To find the amount of the shift, calculate the difference between the y-coordinates of the vertices of f(x) and g(x): 3 - (-1) = 3 + 1 = 4. Since the y-coordinate decreased from 3 to -1, this is a translation 4 units down.

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What kind of transformation converts the graph of $f(x) = -4|x - 7| + 3$ into the graph of $g(x) = -4|x - 7| - 1$ ? $\newline$ Choices: $\newline$ (A) translation $4$ units left $\newline$ (B) translation $4$ units up $\newline$ (C) translation $4$ units right $\newline$ (D) translation $4$ 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) = -4|x - 7| + 3

into the graph of

g(x) = -4|x - 7| - 1

\newline

Choices:

\newline

(A) translation

4

units left

\newline

(B) translation

4

units up

\newline

4

units right

\newline

(D) translation

4

units down

Identify Vertex of $f(x)$ : Identify the vertex of the function $f(x) = -4|x - 7| + 3$ . The vertex of the absolute value function $f(x) = -4|x - 7| + 3$ is at the point where $x - 7 = 0$ , which is $x = 7$ . The $y$ -coordinate of the vertex is the constant term, which is $+3$ . Therefore, the vertex of $f(x)$ is at $(7, 3)$ .
Identify Vertex of $g(x)$ : Identify the vertex of the function $g(x) = -4|x - 7| - 1$ . Similarly, the vertex of the absolute value function $g(x) = -4|x - 7| - 1$ is at the point where $x - 7 = 0$ , which is $x = 7$ . The $y$ -coordinate of the vertex is the constant term, which is $-1$ . Therefore, the vertex of $g(x)$ is at $(7, -1)$ .
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 $+3$ to $-1$ . This is a vertical shift. To find the amount of the shift, calculate the difference between the $y$ -coordinates of the vertices of $f(x)$ and $g(x)$ : $g(x)$ $0$ . Since the $y$ -coordinate decreased from $g(x)$ $2$ to $-1$ , this is a translation $g(x)$ $4$ units down.