Algebra Question

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Step 1

Given four functions are:

  • y=x+5x-3x-3x-2
  • y=1x+3
  • y=x+2x-3
  • y=3xx+2x+2
Step 2
  • Given y=x+5x-3x-3x-2

We can cancel out the factor x-3 from both numerator and denominator.

The function has removable discontinuity at x=3.

So y=x+5x-2

Here degree of both numerator and denominator is same and is equal to 1.

So, it has horizontal asymptote at y=11=1

and vertical asymptote at x-2=0x=2.

Hence the function has both vertical and horizontal asymptotes and a removable discontinuity.

Step 3
  • y=1x+3

Since in the given function the degree of numerator is less than the denominator by 1.

So the horizontal asymptote is y=0.

The vertical asymptote is given by x+3=0x=-3.

The function has vertical asymptote at x=-3 and horizontal asymptote at y=0.

 

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