What kind of transformation converts the graph of f(x) = 9(x + 9)^2 + 10 into the graph of g(x) = 9(x + 4)^2 + 10? Choices: (A)translation 5 units left (B)translation 5 units up (C)translation 5 units down (D)translation 5 units right

Identify Vertex: Identify the vertex of the function f(x). The function f(x) = 9(x + 9)^2 + 10 is in vertex form, where the vertex is at (-9, 10).Determine Transformation Type: Identify the vertex of the function g(x). The function g(x) = 9(x + 4)^2 + 10 is also in vertex form, where the vertex is at (-4, 10).Determine Transformation Direction: Determine the type of transformation. Since the y-coordinate of the vertex remains the same (10) and only the x-coordinate changes, we are dealing with a horizontal transformation.Calculate Horizontal Shift: Determine the direction of the transformation. The x-coordinate of the vertex of f(x) is -9, and the x-coordinate of the vertex of g(x) is -4. Since -4 is to the right of -9 on the number line, the graph has been shifted to the right.Calculate the amount of horizontal shift. The difference in the x-coordinates of the vertices is |-4 - (-9)| = |-4 + 9| = |5| = 5. Therefore, the graph of f(x) has been shifted 5 units to the right to become g(x).

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What kind of transformation converts the graph of $f(x) = 9(x + 9)^2 + 10$ into the graph of $g(x) = 9(x + 4)^2 + 10$ ? $\newline$ Choices: $\newline$ (A) translation $5$ units left $\newline$ (B) translation $5$ units up $\newline$ (C) translation $5$ units down $\newline$ (D) translation $5$ units right

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 9(x + 9)^2 + 10

into the graph of

g(x) = 9(x + 4)^2 + 10

\newline

Choices:

\newline

(A) translation

5

units left

\newline

(B) translation

5

units up

\newline

5

units down

\newline

(D) translation

5

units right

Identify Vertex: Identify the vertex of the function $f(x)$ . The function $f(x) = 9(x + 9)^2 + 10$ is in vertex form, where the vertex is at $(-9, 10)$ .
Determine Transformation Type: Identify the vertex of the function $g(x)$ . The function $g(x) = 9(x + 4)^2 + 10$ is also in vertex form, where the vertex is at $(-4, 10)$ .
Determine Transformation Direction: Determine the type of transformation. $\newline$ Since the $y$ -coordinate of the vertex remains the same ( $10$ ) and only the $x$ -coordinate changes, we are dealing with a horizontal transformation.
Calculate Horizontal Shift: Determine the direction of the transformation. $\newline$ The $x$ -coordinate of the vertex of $f(x)$ is $-9$ , and the $x$ -coordinate of the vertex of $g(x)$ is $-4$ . Since $-4$ is to the right of $-9$ on the number line, the graph has been shifted to the right.
Calculate Horizontal Shift: Determine the direction of the transformation. $\newline$ The x-coordinate of the vertex of $f(x)$ is $-9$ , and the x-coordinate of the vertex of $g(x)$ is $-4$ . Since $-4$ is to the right of $-9$ on the number line, the graph has been shifted to the right.Calculate the amount of horizontal shift. $\newline$ The difference in the x-coordinates of the vertices is $|-4 - (-9)| = |-4 + 9| = |5| = 5$ . Therefore, the graph of $f(x)$ has been shifted $5$ units to the right to become $g(x)$ .