1 / 18

# Solving for the Discontinuities of Rational Equations - PowerPoint PPT Presentation

Solving for the Discontinuities of Rational Equations. Review: 3 Types of Discontinuities. Vertical Asymptotes (VAs) Horizontal Asymptotes (HAs) Holes. Degree. The greatest exponent of an expression Examples: f(x) = x 6 – x 2 + 3 f(x) = x 4 – x 9 + x 11 – x 2 + 5 f(x) = 8x + 4

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

## PowerPoint Slideshow about 'Solving for the Discontinuities of Rational Equations' - salma

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Solving for the Discontinuities of Rational Equations

• Vertical Asymptotes (VAs)

• Horizontal Asymptotes (HAs)

• Holes

• The greatest exponent of an expression

• Examples:

• f(x) = x6 – x2 + 3

• f(x) = x4 – x9 + x11 – x2 + 5

• f(x) = 8x + 4

• f(x) = 7

• The coefficient of the term with the largest degree

• Examples:

• f(x) = x6 – x2 + 3

• f(x) = x4 – x9 + x11 – x2 + 5

• f(x) = 8x + 4

• f(x) = 7

• Remember:

• The horizontal asymptote describes how the graph behaves AT ITS ENDS

• Look for the graph to taper to the same y-value on both ends of the graph

• Look for dashed, horizontal lines

• We DON’T DRAW dashed lines on the X-AXIS or the Y-AXIS!!!

4. What observations can you make about a rational equation’s horizontal asymptote when the degree of the numerator and the denominator are the same?

8. What observations can you make about a rational equation’s horizontal asymptote when the degree of the denominator is greater than the degree of the numerator?

12. What observations can you make about a rational equation’s horizontal asymptote when the degree of the numerator is greater than the degree of the denominator?

• Depend on the degree of the numerator and the denominator

• Degree of Numerator < Degree of Denominator

• HA: y = 0

• Degree of Numerator = Degree of Denominator

• HA: y = ratio of leading coefficients

• Degree of Numerator > Degree of Denominator

• HA: doesn’t exist

• For problems 1 – 4 on the Introduction to Solving Rational Equations Practice, solve for the horizontal asymptote.

1. 2.

3. 4.

• Always factor the numerator and the denominator 1st!

• Identify linear factors in the denominator

• Figure out where the linear factors in the denominator occur the most to decide if you have a vertical asymptote or a hole

• Set the linear factors from step 2 equal to zero and solve for x.

Does the linear factor:

• Complete problems 5 – 12 on the Introduction to Solving for the Discontinuities of Rational Equations Practice handout . BE PREPARED TO SHARE YOUR ANSWERS!!!

• Complete problems 13 – 18.

15. 16.

17. 18.

• Does have a HA? (If yes, what is it?) Why?

• Does have VAs and/or holes? (If yes, what are they?) Why?