1. Advanced Algebra Dr. Shildneck Spring, 2015

2. Things to Remember:  Vertical Asymptotes come from the denominator  Horizontal Asymptotes result from smaller or equal degrees in numerator  Slant Asymptotes result from dividing a 1-degree bigger numerator by the denominator

3. Things to Remember:  Y-Intercepts occur when x = 0.  X-Intercepts (zeros) occur when y = 0.  A General point occurs when x is plugged in to get a y-value.  Holes occur whenever there is a common factor between the numerator and denominator.

4. Things to Remember:  Whenever you are given a specific x-value, it’s related factor is (x – that number).  For example, given x = 5,  It’s factor is (x-5)  And given x = -5,  It’s factor is (x+5)

5.  Determine the vertical asymptotes (VA)  Write a factor for each in the denominator  Determine the horizontal asymptotes (HA)  Determine a factor that would result in that HA based on the rules for asymptotes  If there is a slant asymptote (SA), “un-divide” the numerator and denominator  In other words, multiply.  But! Then, add 1 to the answer.

6.  If there are holes, multiply in a factor in both the numerator and denominator.  If you are given a point (x, y):  make the constant part of the numerator a variable, like (x-b) or (x-h).  Plug in the x-value for x and set equal to the y-value  Solve for your variable constant

7.  Your final answer should be written as a function of x  It should start with “y =“ or “f(x)=“  It should have x variables and numbers. No other letters.  You may leave it in factored form.  Do not multiply out the factors.

8. Write an equation of a rational function with the following characteristics. VA: x = -7 HA: y = 0

9. Write an equation of a rational function with the following characteristics. VA: x = 12 HA: y = 3

10. Write an equation of a rational function with the following characteristics. VA: x = -3 HA: y = 1 Y-int: (0, 5)

11. Write an equation of a rational function with the following characteristics. VA: x = -1 HA: y = 2 Hole at: x = 5

12. Write an equation of a rational function with the following characteristics. VA: x = -1, x = 1 SA: y = 2x-3

13. Worksheet Number 7 Writing Equations of Rational Functions