1. Rational Functions Intro - Chapter 4.4

2.  Let x = ___ to find y – intercepts A rational function is the _______ of two polynomials RATIO Graphs of Rational Functions Step 1: Write in_____________ form.FACTORED Step 2: Find the __________.DOMAIN  It is the set of all real numbers that are not _________ of the denominator ZEROS Step 3: Find the _______________. INTERCEPTS  Let y = ___ to find x – intercepts (when the REDUCED _____________ is zero) 0 NUMERATOR 0 Example 24:

3. Step 4: Find _______________.ASYMPTOTES Vertical Asymptotes:  Find where the ________________ zero. Then find _____________. If _________________, then ________ is a vertical asymptote. DENOMINATOR Horizontal Asymptotes: Find ____________ Example 24:  If ___________ then _____ is a horizontal asymptote  If ____________ then there is an _________asymptote SLANTED

4.  Use ________________ to write the rational function,, into the form ________. ____________ will be the ___________asymptote and ____________________ is used to find the ___________ asymptote. Step 5: Find the points ( x, y ) that are _______ HOLES  The value of x that makes the _____________ and ________________ zero.(same number of factors) NUMERATOR DENOMINATOR  Plug the x into the ___________form of f ( x ) the value of y. REDUCED Example 24: Other Asymptotes: LONG DIVISION SLANTED VERTICAL

5. Step 6: __________ the behavior at the _____________ ANALYZEASYMPTOTES Step 7: ________ any “pretty” points PLOT Example 24:

6. Example 24: Find the sketch of the rational function. Domain: x - intercepts: y - intercept: Vertical Asymptotes: Holes: Horizontal Asymptotes:

7. Horizontal Asymptotes: Pretty Points: Vertical Asymptotes: Asymptote Analysis

8. Example 25: Find the sketch of the rational function. Domain: x - intercepts: y - intercept: Vertical Asymptotes: Other Asymptotes: Holes: Pretty Points: Horizontal Asymptotes: