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What kind of transformation converts the graph of $f(x) = 9|x + 1|$ into the graph of $g(x) = 9|x + 1| - 2$ ? $\newline$ Choices: $\newline$ (A) translation $2$ units down $\newline$ (B) translation $2$ units right $\newline$ (C) translation $2$ units up $\newline$ (D) translation $2$ units left

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Describe function transformations

Full solution

Q. What kind of transformation converts the graph of

f(x) = 9|x + 1|

into the graph of

g(x) = 9|x + 1| - 2

?

\newline

Choices:

\newline

(A) translation

2

units down

\newline

(B) translation

2

units right

\newline

(C) translation

2

units up

\newline

(D) translation

2

units left

Compare Functions: To determine the type of transformation, we need to compare the functions $f(x)$ and $g(x)$ . The function $g(x)$ is obtained from $f(x)$ by subtracting $2$ from it. This means that every $y$ -value of $f(x)$ is decreased by $2$ to get the corresponding $y$ -value of $g(x)$ . This is a vertical shift.
Vertical Shift Explanation: A vertical shift downwards by $k$ units is represented by subtracting $k$ from the function. Since $g(x) = f(x) - 2$ , this corresponds to a vertical shift of $2$ units down.
Eliminate Other Options: We can rule out the other options because they involve horizontal shifts (left or right) or a vertical shift upwards, none of which are represented by subtracting $2$ from the entire function.

More problems from Describe function transformations

Question

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

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\newline

\text{translates it } 4 \text{ units down}

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\newline

\newline

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\newline

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