What kind of transformation converts the graph of f(x) = 4|x - 7| + 6 into the graph of g(x) = 4|x - 9| + 6? Choices: (A)translation 2 units up (B)translation 2 units left (C)translation 2 units right (D)translation 2 units down

Find Vertex of f(x): Find the vertex of the given function f(x). f(x) = 4|x - 7| + 6 has a vertex at x = 7, since that's where the absolute value expression equals zero.Find Vertex of g(x): Find the vertex of the transformed function g(x). g(x) = 4|x - 9| + 6 has a vertex at x = 9, for the same reason as above.Compare Vertex Coordinates: Compare the x-coordinates of the vertices of f(x) and g(x). Vertex of f(x) is at x = 7 and vertex of g(x) is at x = 9.Determine Shift Direction: Determine the direction of the shift from the vertex of f(x) to the vertex of g(x). Since the x-coordinate increased from 7 to 9, the graph shifted to the right.Calculate Shift Magnitude: Calculate the magnitude of the shift. The difference in x-coordinates is 9 - 7 = 2. The graph of f(x) shifts 2 units to the right.

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What kind of transformation converts the graph of $f(x) = 4|x - 7| + 6$ into the graph of $g(x) = 4|x - 9| + 6$ ? $\newline$ Choices: $\newline$ (A) translation $2$ units up $\newline$ (B) translation $2$ units left $\newline$ (C) translation $2$ units right $\newline$ (D) translation $2$ units down

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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) = 4|x - 7| + 6

into the graph of

g(x) = 4|x - 9| + 6

\newline

Choices:

\newline

(A) translation

2

units up

\newline

(B) translation

2

units left

\newline

2

units right

\newline

(D) translation

2

units down

Find Vertex of $f(x)$ : Find the vertex of the given function $f(x)$ . $f(x) = 4|x - 7| + 6$ has a vertex at $x = 7$ , since that's where the absolute value expression equals zero.
Find Vertex of $g(x)$ : Find the vertex of the transformed function $g(x)$ . $g(x) = 4|x - 9| + 6$ has a vertex at $x = 9$ , for the same reason as above.
Compare Vertex Coordinates: Compare the $x$ -coordinates of the vertices of $f(x)$ and $g(x)$ . Vertex of $f(x)$ is at $x = 7$ and vertex of $g(x)$ is at $x = 9$ .
Determine Shift Direction: Determine the direction of the shift from the vertex of $f(x)$ to the vertex of $g(x)$ . Since the $x$ -coordinate increased from $7$ to $9$ , the graph shifted to the right.
Calculate Shift Magnitude: Calculate the magnitude of the shift. $\newline$ The difference in x-coordinates is $9 - 7 = 2$ . $\newline$ The graph of $f(x)$ shifts $2$ units to the right.