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What kind of transformation converts the graph of $f(x) = 6|x + 9| + 5$ into the graph of $g(x) = 6|x + 9| + 1$ ? $\newline$ Choices: $\newline$ (A) translation $4$ units down $\newline$ (B) translation $4$ units up $\newline$ (C) translation $4$ units left $\newline$ (D) translation $4$ units right

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Describe function transformations

Full solution

Q. What kind of transformation converts the graph of

f(x) = 6|x + 9| + 5

into the graph of

g(x) = 6|x + 9| + 1

?

\newline

Choices:

\newline

(A) translation

4

units down

\newline

(B) translation

4

units up

\newline

(C) translation

4

units left

\newline

(D) translation

4

units right

Identify Change Constant Term: Identify the change in the constant term of the function. $\newline$ The function $f(x) = 6|x + 9| + 5$ has a constant term of $+5$ , while the function $g(x) = 6|x + 9| + 1$ has a constant term of $+1$ .
Determine Vertical Shift: Determine the vertical shift required to transform $f(x)$ into $g(x)$ . The change in the constant term from $+5$ to $+1$ indicates a vertical shift. To find the magnitude and direction of this shift, subtract the new constant term from the original constant term: $5 - 1 = 4$ .
Identify Direction Vertical Shift: Identify the direction of the vertical shift. $\newline$ Since the constant term decreased from $+5$ to $+1$ , the graph of $f(x)$ must be shifted downward to obtain the graph of $g(x)$ .
Match Transformation Choices: Match the transformation to the given choices. $\newline$ A downward shift of $4$ units corresponds to the choice (A) translation $4$ units down.

More problems from Describe function transformations

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g(x)

g(x)

is the reflection across the x-axis of

f(x)=9|x+2|-4

\newline

\newline

\text{}(A)g(x) = 9|x+2| - 4\text{]}

\newline

\text{}(B)g(x) = 9|x-2| - 4\text{]}

\newline

\text{}(C)g(x)=-9|x-2| +4\text{]}

\newline

\text{(D)}g(x) = -9|x + 2| + 4\text{]}

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\newline

\newline

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