Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What kind of transformation converts the graph of f(x)=6∣x+9∣+5f(x) = 6|x + 9| + 5 into the graph of g(x)=6∣x+9∣+1g(x) = 6|x + 9| + 1?\newlineChoices:\newline(A) translation 44 units down\newline(B) translation 44 units up\newline(C) translation 44 units left\newline(D) translation 44 units right

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Describe function transformationsright chevron icon

Full solution

Q. What kind of transformation converts the graph of f(x)=6∣x+9∣+5f(x) = 6|x + 9| + 5 into the graph of g(x)=6∣x+9∣+1g(x) = 6|x + 9| + 1?\newlineChoices:\newline(A) translation 44 units down\newline(B) translation 44 units up\newline(C) translation 44 units left\newline(D) translation 44 units right
  1. Identify Change Constant Term: Identify the change in the constant term of the function.\newlineThe function f(x)=6∣x+9∣+5f(x) = 6|x + 9| + 5 has a constant term of +5+5, while the function g(x)=6∣x+9∣+1g(x) = 6|x + 9| + 1 has a constant term of +1+1.
  2. Determine Vertical Shift: Determine the vertical shift required to transform f(x)f(x) into g(x)g(x). The change in the constant term from +5+5 to +1+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=45 - 1 = 4.
  3. Identify Direction Vertical Shift: Identify the direction of the vertical shift.\newlineSince the constant term decreased from +5+5 to +1+1, the graph of f(x)f(x) must be shifted downward to obtain the graph of g(x)g(x).
  4. Match Transformation Choices: Match the transformation to the given choices.\newlineA downward shift of 44 units corresponds to the choice (A) translation 44 units down.

More problems from Describe function transformations

Question
Find g(x)g(x), where g(x)g(x) is the reflection across the x-axis of f(x)=9∣x+2∣−4f(x)=9|x+2|-4.\newlineChoices:\newline(A)g(x)=9∣x+2∣−4]\text{}(A)g(x) = 9|x+2| - 4\text{]}\newline(B)g(x)=9∣x−2∣−4]\text{}(B)g(x) = 9|x-2| - 4\text{]}\newline(C)g(x)=−9∣x−2∣+4]\text{}(C)g(x)=-9|x-2| +4\text{]}\newline(D)g(x)=−9∣x+2∣+4]\text{(D)}g(x) = -9|x + 2| + 4\text{]}
Get tutor helpright-arrow

Posted 9 months ago

Question
What does the transformation f(x)↦f(x−4) f(x) \mapsto f(x - 4) do to the graph of f(x) f(x) ?\newlineChoices:\newline(A) translates it 4 units right\text{translates it } 4 \text{ units right}\newline(B) translates it 4 units down\text{translates it } 4 \text{ units down}\newline(C) translates it 4 units left\text{translates it } 4 \text{ units left}\newline(D) translates it 4 units up\text{translates it } 4 \text{ units up}
Get tutor helpright-arrow

Posted 9 months ago

Question
What does the transformation f(x)↦f(4x) f(x) \mapsto f(4x) do to the graph of f(x) f(x) ?\newlineChoices:\newline[A] stretches it vertically\newline[B] stretches it horizontally\newline[C]shrinks it horizontally\newline[D]shrinks it vertically
Get tutor helpright-arrow

Posted 8 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 99 units down of f(x)=10x+8f(x) = 10x + 8.\newlineChoices:\newline(A) g(x)=10x−82g(x) = 10x - 82 \newline(B) g(x)=10x+98g(x) = 10x + 98 \newline(C) g(x)=10x−1g(x) = 10x - 1\newline(D) g(x)=10x+17g(x) = 10x + 17
Get tutor helpright-arrow

Posted 9 months ago

Question
What kind of transformation converts the graph of f(x)=−3x2−4 f(x) = -3x^2 - 4 into the graph of g(x)=−3x2+6 g(x) = -3x^2 + 6 ?\newlineChoices:\newline[A]translation 10 units up \text{[A]translation 10 units up} \newline[B]translation 10 units down \text{[B]translation 10 units down} \newline[C]translation 10 units left \text{[C]translation 10 units left} \newline[D]translation 10 units right \text{[D]translation 10 units right}
Get tutor helpright-arrow

Posted 8 months ago

Question
The parabola y=x2y=x^{2} is scaled vertically by a factor of 77. What is the equation of the new parabola?\newliney=y=
Get tutor helpright-arrow

Posted 10 months ago

Question
The parabola y=x2y=x^{2} is shifted down by 66 units and to the right by 55 units.\newlineWhat is the equation of the new parabola?\newliney=y=
Get tutor helpright-arrow

Posted 10 months ago

Question
The parabola y=x2y=x^{2} is shifted up by 22 units and to the right by 33 units.\newlineWhat is the equation of the new parabola?\newliney=y=
Get tutor helpright-arrow

Posted 8 months ago

Question
The parabola y=x2 y=x^{2} is reflected across the x x -axis and then scaled vertically by a factor of 55 .\newlineWhat is the equation of the new parabola?\newliney=□ y=\square
Get tutor helpright-arrow

Posted 8 months ago

Question
The parabola y=x2 y=x^{2} is scaled vertically by a factor of 110 \frac{1}{10} .\newlineWhat is the equation of the new parabola?\newliney= y=
Get tutor helpright-arrow

Posted 9 months ago

View all (37)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant