What kind of transformation converts the graph of f(x) = -3(x + 5)^2 - 2 into the graph of g(x) = -3(x + 9)^2 - 2? Choices: (A)translation 4 units right (B)translation 4 units down (C)translation 4 units up (D)translation 4 units left

Identify Vertex: Identify the vertex of the function f(x). The function f(x) = -3(x + 5)^2 - 2 is in vertex form, where the vertex is at the point (-5, -2).Identify Vertex: Identify the vertex of the function g(x). The function g(x) = -3(x + 9)^2 - 2 is also in vertex form, where the vertex is at the point (-9, -2).Type of Transformation: Determine the type of transformation. The y-coordinates of the vertices of f(x) and g(x) are the same, so there is no vertical shift. The x-coordinate of the vertex of g(x) is 4 units to the left of the x-coordinate of the vertex of f(x), indicating a horizontal shift.Direction of Shift: Determine the direction of the horizontal shift. The x-coordinate of the vertex of f(x) is -5, and the x-coordinate of the vertex of g(x) is -9. Since -9 is to the left of -5 on the number line, the graph has shifted to the left.Magnitude of Shift: Calculate the magnitude of the horizontal shift. The difference in the x-coordinates of the vertices is |-5 - (-9)| = |-5 + 9| = |4| = 4. Therefore, the graph of f(x) has shifted 4 units to the left to become the graph of g(x).

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What kind of transformation converts the graph of $f(x) = -3(x + 5)^2 - 2$ into the graph of $g(x) = -3(x + 9)^2 - 2$ ? $\newline$ Choices: $\newline$ (A) translation $4$ units right $\newline$ (B) translation $4$ units down $\newline$ (C) translation $4$ units up $\newline$ (D) translation $4$ units left

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -3(x + 5)^2 - 2

into the graph of

g(x) = -3(x + 9)^2 - 2

\newline

Choices:

\newline

(A) translation

4

units right

\newline

(B) translation

4

units down

\newline

4

units up

\newline

(D) translation

4

units left

Identify Vertex: Identify the vertex of the function $f(x)$ . The function $f(x) = -3(x + 5)^2 - 2$ is in vertex form, where the vertex is at the point $(-5, -2)$ .
Identify Vertex: Identify the vertex of the function $g(x)$ . The function $g(x) = -3(x + 9)^2 - 2$ is also in vertex form, where the vertex is at the point $(-9, -2)$ .
Type of Transformation: Determine the type of transformation. $\newline$ The $y$ -coordinates of the vertices of $f(x)$ and $g(x)$ are the same, so there is no vertical shift. The $x$ -coordinate of the vertex of $g(x)$ is $4$ units to the left of the $x$ -coordinate of the vertex of $f(x)$ , indicating a horizontal shift.
Direction of Shift: Determine the direction of the horizontal shift. The $x$ -coordinate of the vertex of $f(x)$ is $-5$ , and the $x$ -coordinate of the vertex of $g(x)$ is $-9$ . Since $-9$ is to the left of $-5$ on the number line, the graph has shifted to the left.
Magnitude of Shift: Calculate the magnitude of the horizontal shift. The difference in the $x$ -coordinates of the vertices is $|-5 - (-9)| = |-5 + 9| = |4| = 4$ . Therefore, the graph of $f(x)$ has shifted $4$ units to the left to become the graph of $g(x)$ .