What kind of transformation converts the graph of f(x) = -7|x - 3| + 4 into the graph of g(x) = -7|x + 5| + 4? Choices: (A)translation 8 units down (B)translation 8 units left (C)translation 8 units right (D)translation 8 units up

Find Vertex of f(x): Find the vertex of f(x). f(x) = -7|x - 3| + 4 is in the form of y = a|x - h| + k, where (h, k) is the vertex. Vertex of f(x): (3, 4)Find Vertex of g(x): Find the vertex of g(x). g(x) = -7|x + 5| + 4 is in the form of y = a|x - h| + k, where (h, k) is the vertex. Vertex of g(x): (-5, 4)Compare Vertices: Compare the vertices of f(x) and g(x). Vertex of f(x): (3, 4) Vertex of g(x): (-5, 4) The y-coordinates are the same, so the transformation is horizontal.Determine Shift Direction: Determine the direction of the shift. The x-coordinate of the vertex of f(x) is 3, and the x-coordinate of the vertex of g(x) is -5. Since -5 is to the left of 3 on the number line, f(x) shifts to the left.Calculate Shift Amount: Calculate the amount of the shift. |3 - (-5)| = |3 + 5| = |8| = 8 The graph of f(x) shifts 8 units to the left.

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What kind of transformation converts the graph of $f(x) = -7|x - 3| + 4$ into the graph of $g(x) = -7|x + 5| + 4$ ? $\newline$ Choices: $\newline$ (A) translation $8$ units down $\newline$ (B) translation $8$ units left $\newline$ (C) translation $8$ units right $\newline$ (D) translation $8$ units up

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -7|x - 3| + 4

into the graph of

g(x) = -7|x + 5| + 4

\newline

Choices:

\newline

(A) translation

8

units down

\newline

(B) translation

8

units left

\newline

8

units right

\newline

(D) translation

8

units up

Find Vertex of $f(x)$ : Find the vertex of $f(x)$ . $f(x) = -7|x - 3| + 4$ is in the form of $y = a|x - h| + k$ , where $(h, k)$ is the vertex. $Vertex of f(x): (3, 4)$
Find Vertex of g(x): Find the vertex of g(x). $\newline$ g(x) = $-7|x + 5| + 4$ is in the form of $y = a|x - h| + k$ , where $(h, k)$ is the vertex. $\newline$ Vertex of g(x): $(-5, 4)$
Compare Vertices: Compare the vertices of $f(x)$ and $g(x)$ . $\newline$ Vertex of $f(x)$ : $(3, 4)$ $\newline$ Vertex of $g(x)$ : $(-5, 4)$ $\newline$ The $y$ -coordinates are the same, so the transformation is horizontal.
Determine Shift Direction: Determine the direction of the shift. The $x$ -coordinate of the vertex of $f(x)$ is $3$ , and the $x$ -coordinate of the vertex of $g(x)$ is $-5$ . Since $-5$ is to the left of $3$ on the number line, $f(x)$ shifts to the left.
Calculate Shift Amount: Calculate the amount of the shift. $\newline$ $|3 - (-5)| = |3 + 5| = |8| = 8$ $\newline$ The graph of $f(x)$ shifts $8$ units to the left.