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

Analyze Functions: Analyze the given functions to determine the type of transformation. The given functions are f(x) = -|x - 1| - 8 and g(x) = -|x - 2| - 8. We need to compare the inside of the absolute value to see how the graph has shifted.Identify Shift: Identify the shift in the absolute value. The absolute value in f(x) is |x - 1|, and in g(x) it is |x - 2|. The change from |x - 1| to |x - 2| indicates a horizontal shift.Determine Shift Direction: Determine the direction and magnitude of the shift. The shift from |x - 1| to |x - 2| can be seen as adding 1 inside the absolute value, which translates the graph to the right by 1 unit.Verify Vertical Shift: Verify that there is no vertical shift. Both functions have the same vertical translation, -8, which means there is no vertical shift between f(x) and g(x).Conclude Transformation: Conclude the type of transformation. Since the graph has shifted horizontally to the right by 1 unit and there is no vertical shift, the transformation is a translation 1 unit to the right.

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

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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) = -|x - 1| - 8

into the graph of

g(x) = -|x - 2| - 8

\newline

Choices:

\newline

(A) translation

1

unit up

\newline

(B) translation

1

unit down

\newline

1

unit left

\newline

(D) translation

1

unit right

Analyze Functions: Analyze the given functions to determine the type of transformation. The given functions are $f(x) = -|x - 1| - 8$ and $g(x) = -|x - 2| - 8$ . We need to compare the inside of the absolute value to see how the graph has shifted.
Identify Shift: Identify the shift in the absolute value. $\newline$ The absolute value in $f(x)$ is $|x - 1|$ , and in $g(x)$ it is $|x - 2|$ . The change from $|x - 1|$ to $|x - 2|$ indicates a horizontal shift.
Determine Shift Direction: Determine the direction and magnitude of the shift. The shift from $|x - 1|$ to $|x - 2|$ can be seen as adding $1$ inside the absolute value, which translates the graph to the right by $1$ unit.
Verify Vertical Shift: Verify that there is no vertical shift. Both functions have the same vertical translation, $-8$ , which means there is no vertical shift between $f(x)$ and $g(x)$ .
Conclude Transformation: Conclude the type of transformation. $\newline$ Since the graph has shifted horizontally to the right by $1$ unit and there is no vertical shift, the transformation is a translation $1$ unit to the right.