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)=7∣x−2∣−10f(x) = 7|x - 2| - 10 into the graph of g(x)=7∣x+3∣−10g(x) = 7|x + 3| - 10?\newlineChoices:\newline(A) translation 55 units left\newline(B) translation 55 units up\newline(C) translation 55 units right\newline(D) translation 55 units down

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)=7∣x−2∣−10f(x) = 7|x - 2| - 10 into the graph of g(x)=7∣x+3∣−10g(x) = 7|x + 3| - 10?\newlineChoices:\newline(A) translation 55 units left\newline(B) translation 55 units up\newline(C) translation 55 units right\newline(D) translation 55 units down
  1. Identify Vertex f(x)f(x): Identify the vertex of the function f(x)=7∣x−2∣−10f(x) = 7|x - 2| - 10. The vertex of the absolute value function f(x)=a∣x−h∣+kf(x) = a|x - h| + k is (h,k)(h, k). For f(x)=7∣x−2∣−10f(x) = 7|x - 2| - 10, h=2h = 2 and k=−10k = -10. Vertex of f(x)f(x): (2,−10)(2, -10)
  2. Identify Vertex g(x)g(x): Identify the vertex of the function g(x)=7∣x+3∣−10g(x) = 7|x + 3| - 10. The vertex of the absolute value function g(x)=a∣x−h∣+kg(x) = a|x - h| + k is (h,k)(h, k). For g(x)=7∣x+3∣−10g(x) = 7|x + 3| - 10, we can rewrite the inside of the absolute value as x−(−3)x - (-3), so h=−3h = -3 and k=−10k = -10. Vertex of g(x)g(x): (−3,−10)(-3, -10)
  3. Determine Transformation: Determine the transformation from f(x)f(x) to g(x)g(x). The transformation involves a horizontal shift since the xx-coordinates of the vertices are different while the yy-coordinates remain the same. The shift is from x=2x = 2 to x=−3x = -3, which is a movement of 55 units to the 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 3 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 3 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 2 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 3 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 2 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 4 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 4 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 2 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 2 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 3 months ago

View all (38)