What kind of transformation converts the graph of f(x) = 7|x - 2| - 10 into the graph of g(x) = 7|x + 3| - 10? Choices: (A)translation 5 units left (B)translation 5 units up (C)translation 5 units right (D)translation 5 units down

Identify Vertex f(x): Identify the vertex of the function f(x) = 7|x - 2| - 10. The vertex of the absolute value function f(x) = a|x - h| + k is (h, k). For f(x) = 7|x - 2| - 10, h = 2 and k = -10. Vertex of f(x): (2, -10)Identify Vertex g(x): Identify the vertex of the function g(x) = 7|x + 3| - 10. The vertex of the absolute value function g(x) = a|x - h| + k is (h, k). For g(x) = 7|x + 3| - 10, we can rewrite the inside of the absolute value as x - (-3), so h = -3 and k = -10. Vertex of g(x): (-3, -10)Determine Transformation: Determine the transformation from f(x) to g(x). The transformation involves a horizontal shift since the x-coordinates of the vertices are different while the y-coordinates remain the same. The shift is from x = 2 to x = -3, which is a movement of 5 units to the left.

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What kind of transformation converts the graph of $f(x) = 7|x - 2| - 10$ into the graph of $g(x) = 7|x + 3| - 10$ ? $\newline$ Choices: $\newline$ (A) translation $5$ units left $\newline$ (B) translation $5$ units up $\newline$ (C) translation $5$ units right $\newline$ (D) translation $5$ units down

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Math Problems

Algebra 2

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 7|x - 2| - 10

into the graph of

g(x) = 7|x + 3| - 10

\newline

Choices:

\newline

(A) translation

5

units left

\newline

(B) translation

5

units up

\newline

5

units right

\newline

(D) translation

5

units down

Identify Vertex $f(x)$ : Identify the vertex of the function $f(x) = 7|x - 2| - 10$ . The vertex of the absolute value function $f(x) = a|x - h| + k$ is $(h, k)$ . For $f(x) = 7|x - 2| - 10$ , $h = 2$ and $k = -10$ . Vertex of $f(x)$ : $(2, -10)$
Identify Vertex $g(x)$ : Identify the vertex of the function $g(x) = 7|x + 3| - 10$ . The vertex of the absolute value function $g(x) = a|x - h| + k$ is $(h, k)$ . For $g(x) = 7|x + 3| - 10$ , we can rewrite the inside of the absolute value as $x - (-3)$ , so $h = -3$ and $k = -10$ . Vertex of $g(x)$ : $(-3, -10)$
Determine Transformation: Determine the transformation from $f(x)$ to $g(x)$ . The transformation involves a horizontal shift since the $x$ -coordinates of the vertices are different while the $y$ -coordinates remain the same. The shift is from $x = 2$ to $x = -3$ , which is a movement of $5$ units to the left.