Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What kind of transformation converts the graph of $f(x) = -3|x + 8| - 2$ into the graph of $g(x) = -3|x + 8|$ ? $\newline$ Choices: $\newline$ (A) translation $2$ units up $\newline$ (B) translation $2$ units right $\newline$ (C) translation $2$ units down $\newline$ (D) translation $2$ units left

View step-by-step help

View step-by-step help

Describe function transformations

Full solution

Q. What kind of transformation converts the graph of

f(x) = -3|x + 8| - 2

into the graph of

g(x) = -3|x + 8|

?

\newline

Choices:

\newline

(A) translation

2

units up

\newline

(B) translation

2

units right

\newline

(C) translation

2

units down

\newline

(D) translation

2

units left

Identify Structure: Identify the basic structure of the functions $f(x)$ and $g(x)$ . Both functions have the same basic structure, which is a transformation of the absolute value function, scaled by a factor of $-3$ and shifted horizontally by $8$ units to the left. The only difference between $f(x)$ and $g(x)$ is the vertical translation.
Determine Shift: Determine the vertical shift between $f(x)$ and $g(x)$ . The function $f(x) = -3|x + 8| - 2$ is shifted vertically down by $2$ units compared to the function $g(x) = -3|x + 8|$ , which has no vertical shift from the basic structure.
Identify Transformation: Identify the type of transformation based on the vertical shift. Since $f(x)$ is shifted down by $2$ units to become $g(x)$ , the transformation is a translation $2$ units up.
Match Choices: Match the transformation to the given choices. $\newline$ The correct transformation is a translation $2$ units up, which corresponds to choice $(A)$ .

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{]}

Posted 3 months ago

Question

What does the transformation

f(x) \mapsto f(x - 4)

do to the graph of

f(x)

\newline

\newline

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

\newline

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

\newline

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

\newline

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

Posted 3 months ago

Question

What does the transformation

f(x) \mapsto f(4x)

do to the graph of

f(x)

\newline

\newline

[A] stretches it vertically

\newline

[B] stretches it horizontally

\newline

[C]shrinks it horizontally

\newline

[D]shrinks it vertically

Posted 2 months ago

Question

g(x)

g(x)

is the translation

9

f(x) = 10x + 8

\newline

\newline

g(x) = 10x - 82

\newline

g(x) = 10x + 98

\newline

g(x) = 10x - 1

\newline

g(x) = 10x + 17

Posted 3 months ago

Question

What kind of transformation converts the graph of

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

into the graph of

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

\newline

\newline

\text{[A]translation 10 units up}

\newline

\text{[B]translation 10 units down}

\newline

\text{[C]translation 10 units left}

\newline

\text{[D]translation 10 units right}

Posted 2 months ago

Question

y=x^{2}

is scaled vertically by a factor of

7

. What is the equation of the new parabola?

\newline

y=

Posted 4 months ago

Question

y=x^{2}

is shifted down by

6

units and to the right by

5

\newline

What is the equation of the new parabola?

\newline

y=

Posted 4 months ago

Question

y=x^{2}

is shifted up by

2

units and to the right by

3

\newline

What is the equation of the new parabola?

\newline

y=

Posted 2 months ago

Question

y=x^{2}

is reflected across the

x

-axis and then scaled vertically by a factor of

5

\newline

What is the equation of the new parabola?

\newline

y=\square

Posted 2 months ago

Question

y=x^{2}

is scaled vertically by a factor of

\frac{1}{10}

\newline

What is the equation of the new parabola?

\newline

y=

Posted 3 months ago