What kind of transformation converts the graph of f(x) = 6|x - 7| - 2 into the graph of g(x) = 6|x - 7| + 1? Choices: (A)translation 3 units left (B)translation 3 units right (C)translation 3 units up (D)translation 3 units down

Identify Function Forms: Identify the basic form of the functions and the transformation involved. The function f(x) = 6|x - 7| - 2 is an absolute value function with a vertex at (7, -2). The function g(x) = 6|x - 7| + 1 is also an absolute value function with the same slope and opening direction, but with a different y-intercept.Determine Vertical Shift: Determine the vertical shift between the two functions. The only difference between f(x) and g(x) is the constant term at the end of the equation. The constant term in f(x) is -2, and in g(x) it is +1. To go from -2 to +1, you need to add 3.Identify Transformation Type: Identify the type of transformation based on the change in the constant term. Adding 3 to the constant term corresponds to a vertical shift upwards by 3 units.Match Transformation to Choices: Match the transformation to the given choices. The transformation that converts f(x) to g(x) is a translation 3 units up, which matches choice (C).

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What kind of transformation converts the graph of $f(x) = 6|x - 7| - 2$ into the graph of $g(x) = 6|x - 7| + 1$ ? $\newline$ Choices: $\newline$ (A) translation $3$ units left $\newline$ (B) translation $3$ units right $\newline$ (C) translation $3$ units up $\newline$ (D) translation $3$ units down

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Algebra 2

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 6|x - 7| - 2

into the graph of

g(x) = 6|x - 7| + 1

\newline

Choices:

\newline

(A) translation

3

units left

\newline

(B) translation

3

units right

\newline

3

units up

\newline

(D) translation

3

units down

Identify Function Forms: Identify the basic form of the functions and the transformation involved. $\newline$ The function $f(x) = 6|x - 7| - 2$ is an absolute value function with a vertex at $(7, -2)$ . The function $g(x) = 6|x - 7| + 1$ is also an absolute value function with the same slope and opening direction, but with a different y-intercept.
Determine Vertical Shift: Determine the vertical shift between the two functions. $\newline$ The only difference between $f(x)$ and $g(x)$ is the constant term at the end of the equation. The constant term in $f(x)$ is $-2$ , and in $g(x)$ it is $+1$ . To go from $-2$ to $+1$ , you need to add $3$ .
Identify Transformation Type: Identify the type of transformation based on the change in the constant term. Adding $3$ to the constant term corresponds to a vertical shift upwards by $3$ units.
Match Transformation to Choices: Match the transformation to the given choices. $\newline$ The transformation that converts $f(x)$ to $g(x)$ is a translation $3$ units up, which matches choice (C).