What kind of transformation converts the graph of f(x) = -7|x - 1| - 2 into the graph of g(x) = -7|x - 1| - 10? Choices: (A)translation 8 units up (B)translation 8 units right (C)translation 8 units left (D)translation 8 units down

Identify Transformation Type: Analyze the given functions f(x) = -7|x - 1| - 2 and g(x) = -7|x - 1| - 10 to determine the type of transformation. Since the absolute value expression -7|x - 1| remains unchanged and only the constant term changes from -2 to -10, this indicates a vertical shift.Determine Vertical Shift Direction: Determine the direction of the vertical shift. The constant term in f(x) is -2, and in g(x) it is -10. Since -10 is less than -2, the graph has shifted downwards.Calculate Vertical Shift Magnitude: Calculate the magnitude of the vertical shift. The change in the constant term from f(x) to g(x) is from -2 to -10, which is a change of -10 - (-2) = -8. This means the graph has shifted 8 units down.

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What kind of transformation converts the graph of $f(x) = -7|x - 1| - 2$ into the graph of $g(x) = -7|x - 1| - 10$ ? $\newline$ Choices: $\newline$ (A) translation $8$ units up $\newline$ (B) translation $8$ units right $\newline$ (C) translation $8$ units left $\newline$ (D) translation $8$ units down

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -7|x - 1| - 2

into the graph of

g(x) = -7|x - 1| - 10

\newline

Choices:

\newline

(A) translation

8

units up

\newline

(B) translation

8

units right

\newline

8

units left

\newline

(D) translation

8

units down

Identify Transformation Type: Analyze the given functions $f(x) = -7|x - 1| - 2$ and $g(x) = -7|x - 1| - 10$ to determine the type of transformation. $\newline$ Since the absolute value expression $-7|x - 1|$ remains unchanged and only the constant term changes from $-2$ to $-10$ , this indicates a vertical shift.
Determine Vertical Shift Direction: Determine the direction of the vertical shift. The constant term in $f(x)$ is $-2$ , and in $g(x)$ it is $-10$ . Since $-10$ is less than $-2$ , the graph has shifted downwards.
Calculate Vertical Shift Magnitude: Calculate the magnitude of the vertical shift. $\newline$ The change in the constant term from $f(x)$ to $g(x)$ is from $-2$ to $-10$ , which is a change of $-10 - (-2) = -8$ . This means the graph has shifted $8$ units down.