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

Identify Vertex of f(x): Identify the vertex of the function f(x) = -7|x + 4| + 7. The vertex of the absolute value function f(x) = -7|x + 4| + 7 occurs where the expression inside the absolute value is zero, i.e., x + 4 = 0, which gives x = -4. The y-coordinate of the vertex is the constant term outside the absolute value, which is +7. Therefore, the vertex of f(x) is (-4, 7).Identify Vertex of g(x): Identify the vertex of the function g(x) = -7|x - 3| + 7. Similarly, the vertex of the absolute value function g(x) = -7|x - 3| + 7 occurs where the expression inside the absolute value is zero, i.e., x - 3 = 0, which gives x = 3. The y-coordinate of the vertex is the same as in f(x), which is +7. Therefore, the vertex of g(x) is (3, 7).Determine Transformation: Determine the transformation from f(x) to g(x). The transformation from f(x) to g(x) involves a horizontal shift from the vertex (-4, 7) to the vertex (3, 7). The shift is to the right by 7 units since -4 + 7 = 3.

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

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Algebra 2

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -7|x + 4| + 7

into the graph of

g(x) = -7|x - 3| + 7

\newline

Choices:

\newline

(A) translation

7

units down

\newline

(B) translation

7

units right

\newline

7

units left

\newline

(D) translation

7

units up

Identify Vertex of $f(x)$ : Identify the vertex of the function $f(x) = -7|x + 4| + 7$ . The vertex of the absolute value function $f(x) = -7|x + 4| + 7$ occurs where the expression inside the absolute value is zero, i.e., $x + 4 = 0$ , which gives $x = -4$ . The y-coordinate of the vertex is the constant term outside the absolute value, which is $+7$ . Therefore, the vertex of $f(x)$ is $(-4, 7)$ .
Identify Vertex of $g(x)$ : Identify the vertex of the function $g(x) = -7|x - 3| + 7$ . Similarly, the vertex of the absolute value function $g(x) = -7|x - 3| + 7$ occurs where the expression inside the absolute value is zero, i.e., $x - 3 = 0$ , which gives $x = 3$ . The $y$ -coordinate of the vertex is the same as in $f(x)$ , which is $+7$ . Therefore, the vertex of $g(x)$ is $(3, 7)$ .
Determine Transformation: Determine the transformation from $f(x)$ to $g(x)$ . The transformation from $f(x)$ to $g(x)$ involves a horizontal shift from the vertex $(-4, 7)$ to the vertex $(3, 7)$ . The shift is to the right by $7$ units since $-4 + 7 = 3$ .