Download presentation

Presentation is loading. Please wait.

1
Rational Functions

2
**Definition: A Rational Function is a function in the form:**

f(x) = where p(x) and q(x) are polynomial functions and q(x) ≠ 0. In this section, p and q will have degree 1 or 0. For example:

3
**Very Important definitions:**

Vertical asymptote occurs at values of x for which the function is undefined (exception: unless there is a hole we’ll talk about that later). Horizontal asymptote occurs if the function approaches a specific value when x approaches infinity or negative infinity. Think of the warmup: what happens to y when x gets REALLY big or REALLY small? To graph rational functions, ALWAYS figure out the asymptotes FIRST. Then you can plot specific points!!!!

4
**Vertical asymptote will occur at x = 0.**

Consider: Vertical asymptote will occur at x = 0. Df = (, 0), (0, ) Horizontal asymptote will occur at y = 0. Think what happens when you divide 1 by a VERY large number!!!!! Show your asymptotes!! Pick some x’s on each side of the vertical asymptote to see the graph!!!

5
**Note: the graph represents a hyperbola centered at (0, 0)**

x y Y −3 3 −2 2 −1 1 −.5 .5 -.3333 .3333 -.5 .5 -1 1 -2 2 In most cases, the range will be closely related to the horizontal asymptote be sure to check the graph. Rf = (, 0), (0, ) Note: the graph represents a hyperbola centered at (0, 0)

6
**Another type of rational function:**

The vertical asymptote is still x = h. Df = (, h), (h, ) Based on our observations, the hortizontal asymptote is y = k. So, this will be a hyperbola centered at (h, k)!!

7
**Vertical asymptote: x = –3**

Horizontal asymptote: y = 2 Show your asymptotes!! Pick some x’s on each side of the vertical asymptote to see the graph!!! x y Y −4 –2 −5 –1 4 1 3 Use more points if you want . . . Df = (, 3), (3, ) Rf = (, 2), (2, )

8
**Last example: Asymptotes: x = –2 y = 3 8 –2 5.5 .5**

Vertical asymptote will correspond to the value that makes the denominator 0. Horizontal asymptote: y = Asymptotes: x = –2 y = 3 x y Y −3 –1 −4 8 –2 5.5 .5 Df = (, 2), (2, ) Rf = (, 3), (3, )

9
x = 0; y = 0 x = 3; y = 1

10
x = 4; y = 1 Remember: Find the asymptotes FIRST. Show them on the graph!!! Pick x values to the right and to the left of the vertical asymptote(s). Use the points along with the asymptotes to sketch the graph!!!

Similar presentations

OK

Rational Functions Learning Objective: To find vertical asymptotes, horizontal asymptotes, holes, and one or two key points, then graph rational functions.

Rational Functions Learning Objective: To find vertical asymptotes, horizontal asymptotes, holes, and one or two key points, then graph rational functions.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on credit default swaps and the financial crisis Download ppt on pulse code modulation Full ppt on electron beam machining ppt Ppt on total internal reflection evanescence Ppt on rainwater harvesting techniques Ppt on non agricultural activities for kids Download ppt on heating effect of electric current Download ppt on ohm's law for class 10 Ppt on video teleconferencing for social security Slideshare ppt on marketing