What kind of transformation converts the graph of f(x) = 2|x - 1| + 1 into the graph of g(x) = 2|x - 9| + 1? Choices: (A)translation 8 units right (B)translation 8 units down (C)translation 8 units up (D)translation 8 units left

Identify vertex function: Identify the vertex of the function f(x). The function f(x) = 2|x - 1| + 1 is in the form of an absolute value function, which has a vertex at the point where the expression inside the absolute value is zero. Set x - 1 = 0 to find the x-coordinate of the vertex of f(x). x = 1 The vertex of f(x) is at (1, 1 + 1) = (1, 2).Set x-coordinate vertex: Identify the vertex of the function g(x). The function g(x) = 2|x - 9| + 1 is also in the form of an absolute value function, which has a vertex at the point where the expression inside the absolute value is zero. Set x - 9 = 0 to find the x-coordinate of the vertex of g(x). x = 9 The vertex of g(x) is at (9, 1 + 1) = (9, 2).Determine transformation type: Determine the type of transformation. We have the vertices of f(x) and g(x) as (1, 2) and (9, 2), respectively. Since the y-coordinates of the vertices are the same, there is no vertical transformation. The x-coordinate of the vertex of g(x) is 8 units greater than the x-coordinate of the vertex of f(x), indicating a horizontal transformation.Determine direction transformation: Determine the direction of the horizontal transformation. The x-coordinate of the vertex of g(x) is greater than the x-coordinate of the vertex of f(x), which means the graph has been shifted to the right. The amount of shift is the difference in the x-coordinates of the vertices, which is 9 - 1 = 8 units.Choose correct transformation: Choose the correct transformation from the given choices. The graph of f(x) has been shifted 8 units to the right to obtain the graph of g(x). The correct choice is (A) translation 8 units right.

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What kind of transformation converts the graph of $f(x) = 2|x - 1| + 1$ into the graph of $g(x) = 2|x - 9| + 1$ ? $\newline$ Choices: $\newline$ (A) translation $8$ units right $\newline$ (B) translation $8$ units down $\newline$ (C) translation $8$ units up $\newline$ (D) translation $8$ 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| + 1

into the graph of

g(x) = 2|x - 9| + 1

\newline

Choices:

\newline

(A) translation

8

units right

\newline

(B) translation

8

units down

\newline

8

units up

\newline

(D) translation

8

units left

Identify vertex function: Identify the vertex of the function $f(x)$ . The function $f(x) = 2|x - 1| + 1$ is in the form of an absolute value function, which has a vertex at the point where the expression inside the absolute value is zero. Set $x - 1 = 0$ to find the $x$ -coordinate of the vertex of $f(x)$ . $x = 1$ The vertex of $f(x)$ is at $(1, 1 + 1) = (1, 2)$ .
Set x-coordinate vertex: Identify the vertex of the function $g(x)$ . The function $g(x) = 2|x - 9| + 1$ is also in the form of an absolute value function, which has a vertex at the point where the expression inside the absolute value is zero. Set $x - 9 = 0$ to find the x-coordinate of the vertex of $g(x)$ . $x = 9$ The vertex of $g(x)$ is at $(9, 1 + 1) = (9, 2)$ .
Determine transformation type: Determine the type of transformation. $\newline$ We have the vertices of $f(x)$ and $g(x)$ as $(1, 2)$ and $(9, 2)$ , respectively. $\newline$ Since the $y$ -coordinates of the vertices are the same, there is no vertical transformation. $\newline$ The $x$ -coordinate of the vertex of $g(x)$ is $8$ units greater than the $x$ -coordinate of the vertex of $f(x)$ , indicating a horizontal transformation.
Determine direction transformation: Determine the direction of the horizontal transformation. $\newline$ The $x$ -coordinate of the vertex of $g(x)$ is greater than the $x$ -coordinate of the vertex of $f(x)$ , which means the graph has been shifted to the right. $\newline$ The amount of shift is the difference in the $x$ -coordinates of the vertices, which is $9 - 1 = 8$ units.
Choose correct transformation: Choose the correct transformation from the given choices. $\newline$ The graph of $f(x)$ has been shifted $8$ units to the right to obtain the graph of $g(x)$ . $\newline$ The correct choice is (A) translation $8$ units right.