What kind of transformation converts the graph of f(x) = 2|x + 1| + 4 into the graph of g(x) = 2|x + 10| + 4? Choices: (A)translation 9 units right (B)translation 9 units up (C)translation 9 units down (D)translation 9 units left

Identify Basic Form: Identify the basic form of the functions and the effect of the absolute value transformation. The basic form of the function is f(x) = a|x - h| + k, where (h, k) is the vertex of the graph. For f(x) = 2|x + 1| + 4, the vertex is at (-1, 4).Identify Vertex: Identify the vertex of the transformed function g(x). For g(x) = 2|x + 10| + 4, the vertex is at (-10, 4).Determine Transformation Type: Determine the type of transformation by comparing the vertices of f(x) and g(x). The vertex of f(x) is (-1, 4) and the vertex of g(x) is (-10, 4). The y-coordinates are the same, so there is no vertical shift. The x-coordinate has changed from -1 to -10, which indicates a horizontal shift.Calculate Horizontal Shift: Calculate the horizontal shift from the vertex of f(x) to the vertex of g(x). The shift is from -1 to -10, which is a movement to the left on the x-axis. The amount of shift is |-1 - (-10)| = |9| = 9 units to the left.

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What kind of transformation converts the graph of $f(x) = 2|x + 1| + 4$ into the graph of $g(x) = 2|x + 10| + 4$ ? $\newline$ Choices: $\newline$ (A) translation $9$ units right $\newline$ (B) translation $9$ units up $\newline$ (C) translation $9$ units down $\newline$ (D) translation $9$ units left

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Math Problems

Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 2|x + 1| + 4

into the graph of

g(x) = 2|x + 10| + 4

\newline

Choices:

\newline

(A) translation

9

units right

\newline

(B) translation

9

units up

\newline

9

units down

\newline

(D) translation

9

units left

Identify Basic Form: Identify the basic form of the functions and the effect of the absolute value transformation. $\newline$ The basic form of the function is $f(x) = a|x - h| + k$ , where $(h, k)$ is the vertex of the graph. For $f(x) = 2|x + 1| + 4$ , the vertex is at $(-1, 4)$ .
Identify Vertex: Identify the vertex of the transformed function $g(x)$ . For $g(x) = 2|x + 10| + 4$ , the vertex is at $(-10, 4)$ .
Determine Transformation Type: Determine the type of transformation by comparing the vertices of $f(x)$ and $g(x)$ . The vertex of $f(x)$ is $(-1, 4)$ and the vertex of $g(x)$ is $(-10, 4)$ . The $y$ -coordinates are the same, so there is no vertical shift. The $x$ -coordinate has changed from $-1$ to $-10$ , which indicates a horizontal shift.
Calculate Horizontal Shift: Calculate the horizontal shift from the vertex of $f(x)$ to the vertex of $g(x)$ . The shift is from $-1$ to $-10$ , which is a movement to the left on the x-axis. The amount of shift is $|-1 - (-10)| = |9| = 9$ units to the left.