What kind of transformation converts the graph of f(x) = (x + 4)^2 + 8 into the graph of g(x) = (x - 4)^2 + 8? Choices: (A)translation 8 units left (B)translation 8 units up (C)translation 8 units down (D)translation 8 units right

Identify Vertex: Identify the vertex of the function f(x). The function f(x) = (x + 4)^2 + 8 is in vertex form, where the vertex is at (-4, 8).Determine Transformation Type: Identify the vertex of the function g(x). The function g(x) = (x - 4)^2 + 8 is also in vertex form, where the vertex is at (4, 8).Determine Shift Direction: Determine the type of transformation. The y-coordinates of the vertices of f(x) and g(x) are the same, which means there is no vertical shift. The x-coordinates of the vertices have changed from -4 to 4, indicating a horizontal shift.Calculate Shift Magnitude: Determine the direction of the horizontal shift. The x-coordinate of the vertex of f(x) is -4, and the x-coordinate of the vertex of g(x) is 4. Since the x-coordinate has increased, the graph has shifted to the right.Calculate the magnitude of the horizontal shift. The difference in the x-coordinates of the vertices is 4 - (-4) = 8 units. Therefore, the graph of f(x) has been shifted 8 units to the right to obtain the graph of g(x).

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What kind of transformation converts the graph of $f(x) = (x + 4)^2 + 8$ into the graph of $g(x) = (x - 4)^2 + 8$ ? $\newline$ Choices: $\newline$ (A) translation $8$ units left $\newline$ (B) translation $8$ units up $\newline$ (C) translation $8$ units down $\newline$ (D) translation $8$ 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) = (x + 4)^2 + 8

into the graph of

g(x) = (x - 4)^2 + 8

\newline

Choices:

\newline

(A) translation

8

units left

\newline

(B) translation

8

units up

\newline

8

units down

\newline

(D) translation

8

units right

Identify Vertex: Identify the vertex of the function $f(x)$ . The function $f(x) = (x + 4)^2 + 8$ is in vertex form, where the vertex is at $(-4, 8)$ .
Determine Transformation Type: Identify the vertex of the function $g(x)$ . The function $g(x) = (x - 4)^2 + 8$ is also in vertex form, where the vertex is at $(4, 8)$ .
Determine Shift Direction: Determine the type of transformation. $\newline$ The $y$ -coordinates of the vertices of $f(x)$ and $g(x)$ are the same, which means there is no vertical shift. The $x$ -coordinates of the vertices have changed from $-4$ to $4$ , indicating a horizontal shift.
Calculate Shift Magnitude: Determine the direction of the horizontal shift. The $x$ -coordinate of the vertex of $f(x)$ is $-4$ , and the $x$ -coordinate of the vertex of $g(x)$ is $4$ . Since the $x$ -coordinate has increased, the graph has shifted to the right.
Calculate Shift Magnitude: Determine the direction of the horizontal shift. The $x$ -coordinate of the vertex of $f(x)$ is $-4$ , and the $x$ -coordinate of the vertex of $g(x)$ is $4$ . Since the $x$ -coordinate has increased, the graph has shifted to the right.Calculate the magnitude of the horizontal shift. The difference in the $x$ -coordinates of the vertices is $4 - (-4) = 8$ units. Therefore, the graph of $f(x)$ has been shifted $f(x)$ $0$ units to the right to obtain the graph of $g(x)$ .