{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MTH 163 Asymptotes Tutorial

# MTH 163 Asymptotes Tutorial - ASYMPTOTES TUTORIAL...

This preview shows pages 1–9. Sign up to view the full content.

ASYMPTOTES TUTORIAL Horizontal Vertical Slant and Holes

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Definition of an asymptote An asymptote is a straight line which acts as a boundary for the graph of a function. When a function has an asymptote (and not all functions have them) the function gets closer and closer to the asymptote as the input value to the function approaches either a specific value a or positive or negative infinity. The functions most likely to have asymptotes are rational functions
Vertical Asymptotes Vertical asymptotes occur when the following condition is met: The denominator of the simplified rational function is equal to 0. Remember, the simplified rational function has cancelled any factors common to both the numerator and denominator.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Finding Vertical Asymptotes Example 1 Given the function The first step is to cancel any factors common to both numerator and denominator. In this case there are none. The second step is to see where the denominator of the simplified function equals 0. ( 29 x x x f 2 2 5 2 + - = ( 29 1 0 1 0 1 2 0 2 2 - = = + = + = + x x x x
Finding Vertical Asymptotes Example 1 Con’t. The vertical line x = -1 is the only vertical asymptote for the function. As the input value x to this function gets closer and closer to -1 the function itself looks and acts more and more like the vertical line x = -1.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Graph of Example 1 The vertical dotted line at x = –1 is the vertical asymptote.
Finding Vertical Asymptotes Example 2 If First simplify the function. Factor both numerator and denominator and cancel any common factors. ( 29 9 12 10 2 2 2 - + + = x x x x f ( 29 ( 29 ( 29 ( 29 3 4 2 3 3 4 2 3 9 12 10 2 3 2 - + = - + + + = - + + x x x x x x x x x

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Finding Vertical Asymptotes Example 2 Con’t.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern