aa6223017
Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

1.consider the function
F(x)=log3x and g(x)=4log3( x+1 ) and answer the following questions

A. Describe each of the transformations required to transform the graph of f(x) to g(x)

B. Using the transformations you described above, draw a scetch of g(x). (On a graph)

C. Describe and give the equations for any asymptotes

D. List any x and y intercepts for any asymptotes and What is the behavior of g(x)?

Sagot :

MrRoyal

Function transformation involves changing the form of a function

  • The transformation from f(x) to g(x) is a horizontal shift 3 units left, followed by a vertical stretch by a factor of 4
  • The x and y intercepts are -0.67 and 1.91, respectively.
  • The behavior of g(x) is that, g(x) approaches infinity, as x approaches infinity.

The functions are given as:

[tex]\mathbf{f(x) = log3x}[/tex]

[tex]\mathbf{g(x) = 4log3(x+1)}[/tex]

(a) The transformation from f(x) to g(x)

First, f(x) is shifted left by 1 unit.

The rule of this transformation is:

[tex]\mathbf{(x,y) \to (x + 1,y)}[/tex]

So, we have:

[tex]\mathbf{f'(x) = log3(x + 1)}[/tex]

Next. f'(x) is vertically stretched by a factor of 4.

The rule of this transformation is:

[tex]\mathbf{(x,y) \to (x,4y)}[/tex]

So, we have:

[tex]\mathbf{g(x) = 4log3(x+1)}[/tex]

Hence, the transformation from f(x) to g(x) is a horizontal shift 3 units left, followed by a vertical stretch by a factor of 4

(b) Sketch of g(x)

See attachment

(c) Asymptotes

The graphs of g(x) have no asymptote

(d) The intercepts, and the behavior of f(x)

The graph crosses the x-axis at x =-0.67, and it crosses the y-axis at y = 1.91

Hence, the x and y intercepts are -0.67 and 1.91, respectively.

The behavior of g(x) is that, g(x) approaches infinity, as x approaches infinity.

We know this because, the value of the function increases as x increases

Read more about function transformations at:

https://brainly.com/question/13810353

View image MrRoyal
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.