What kind of transformation converts the graph of f(x) = 6|x + 1| + 8 into the graph of g(x) = 6|x + 1| - 1? Choices: (A)translation 9 units left (B)translation 9 units up (C)translation 9 units right (D)translation 9 units down

Identify Basic Form: Identify the basic form of the functions and the transformation involved. The function f(x) = 6|x + 1| + 8 is a vertical translation of the parent function 6|x| by 8 units up and 1 unit left. The function g(x) = 6|x + 1| - 1 is also a vertical translation of the parent function 6|x| but with a different vertical shift.Determine Vertical Shift: Determine the vertical shift between the two functions. The vertical shift can be found by comparing the constant terms of f(x) and g(x). The constant term in f(x) is +8, and the constant term in g(x) is -1.Calculate Shift Difference: Calculate the difference in the vertical shift. The difference in the vertical shift is -1 - (+8) = -9. This means that the graph of g(x) is shifted 9 units down from the graph of f(x).

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What kind of transformation converts the graph of $f(x) = 6|x + 1| + 8$ into the graph of $g(x) = 6|x + 1| - 1$ ? $\newline$ Choices: $\newline$ (A) translation $9$ units left $\newline$ (B) translation $9$ units up $\newline$ (C) translation $9$ units right $\newline$ (D) translation $9$ 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 + 1| + 8

into the graph of

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

\newline

Choices:

\newline

(A) translation

9

units left

\newline

(B) translation

9

units up

\newline

9

units right

\newline

(D) translation

9

units down

Identify Basic Form: Identify the basic form of the functions and the transformation involved. $\newline$ The function $f(x) = 6|x + 1| + 8$ is a vertical translation of the parent function $6|x|$ by $8$ units up and $1$ unit left. The function $g(x) = 6|x + 1| - 1$ is also a vertical translation of the parent function $6|x|$ but with a different vertical shift.
Determine Vertical Shift: Determine the vertical shift between the two functions. The vertical shift can be found by comparing the constant terms of $f(x)$ and $g(x)$ . The constant term in $f(x)$ is $+8$ , and the constant term in $g(x)$ is $-1$ .
Calculate Shift Difference: Calculate the difference in the vertical shift. $\newline$ The difference in the vertical shift is $-1 - (+8) = -9$ . This means that the graph of $g(x)$ is shifted $9$ units down from the graph of $f(x)$ .