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)=5∣x+10∣−6f(x) = 5|x + 10| - 6 into the graph of g(x)=5∣x+5∣−6g(x) = 5|x + 5| - 6?\newlineChoices:\newline(A) translation 55 units down\newline(B) translation 55 units up\newline(C) translation 55 units left\newline(D) translation 55 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)=5∣x+10∣−6f(x) = 5|x + 10| - 6 into the graph of g(x)=5∣x+5∣−6g(x) = 5|x + 5| - 6?\newlineChoices:\newline(A) translation 55 units down\newline(B) translation 55 units up\newline(C) translation 55 units left\newline(D) translation 55 units right
  1. Identify Transformation: Identify the transformation affecting the absolute value expression.\newlineThe absolute value function f(x)=5∣x+10∣−6f(x) = 5|x + 10| - 6 has been changed to g(x)=5∣x+5∣−6g(x) = 5|x + 5| - 6. The change is inside the absolute value from ∣x+10∣|x + 10| to ∣x+5∣|x + 5|. This suggests a horizontal shift.
  2. Determine Shift Direction: Determine the direction and magnitude of the horizontal shift. The expression inside the absolute value has changed from (x+10)(x + 10) to (x+5)(x + 5). This indicates a shift to the left by 55 units because the value added to xx has decreased by 55.
  3. Match Transformation to Choices: Match the transformation to the given choices.\newlineThe transformation is a horizontal shift to the left by 55 units. This corresponds to choice (C) translation 55 units left.

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