- By
**salma** - Follow User

- 69 Views
- Uploaded on

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

Review: 3 Types of Discontinuities

- Vertical Asymptotes (VAs)
- Horizontal Asymptotes (HAs)
- Holes

Degree

- 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

Leading Coefficient

- 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

Horizontal Asymptotes Investigation

- 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!!!

Investigation Conclusion Questions:

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?

*Horizontal Asymptotes

- 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

Your Turn:

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

1. 2.

3. 4.

Solving for Vertical Asymptotes and Holes

- 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.

Solving for Vertical Asymptotes and Holes, cont.

Does the linear factor:

Your Turn:

- 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.

Exit Ticket

- Does have a HA? (If yes, what is it?) Why?
- Does have VAs and/or holes? (If yes, what are they?) Why?

Download Presentation

Connecting to Server..