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What kind of transformation converts the graph of $f(x) = -3|x + 10| - 8$ into the graph of $g(x) = -3|x + 10| - 9$ ? $\newline$ Choices: $\newline$ (A) translation $1$ unit right $\newline$ (B) translation $1$ unit down $\newline$ (C) translation $1$ unit left $\newline$ (D) translation $1$ unit up

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Describe function transformations

Full solution

Q. What kind of transformation converts the graph of

f(x) = -3|x + 10| - 8

into the graph of

g(x) = -3|x + 10| - 9

?

\newline

Choices:

\newline

(A) translation

1

unit right

\newline

(B) translation

1

unit down

\newline

(C) translation

1

unit left

\newline

(D) translation

1

unit up

Identify Basic Form: Identify the basic form of the functions and determine the type of transformation based on the difference between $f(x)$ and $g(x)$ . $f(x) = -3|x + 10| - 8$ $g(x) = -3|x + 10| - 9$ The only difference between $f(x)$ and $g(x)$ is the constant term at the end of the equation. This indicates a vertical shift.
Determine Vertical Shift: Determine the direction and magnitude of the vertical shift. $\newline$ The constant term in $f(x)$ is $-8$ , and in $g(x)$ it is $-9$ . Since $-9$ is one unit less than $-8$ , this means the graph of $g(x)$ is shifted down by $1$ unit compared to the graph of $f(x)$ .
Match Transformation: Match the transformation to the given choices. $\newline$ The graph of $g(x)$ is the graph of $f(x)$ shifted down by $1$ unit. This corresponds to choice (B) translation $1$ unit down.

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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What does the transformation

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\newline

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

\newline

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

\newline

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

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[A] stretches it vertically

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[B] stretches it horizontally

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[C]shrinks it horizontally

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[D]shrinks it vertically

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g(x)

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\newline

\newline

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\newline

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\newline

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Question

What kind of transformation converts the graph of

f(x) = -3x^2 - 4

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g(x) = -3x^2 + 6

\newline

\newline

\text{[A]translation 10 units up}

\newline

\text{[B]translation 10 units down}

\newline

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\text{[D]translation 10 units right}

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y=x^{2}

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y=x^{2}

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y=x^{2}

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y=x^{2}

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y=x^{2}

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