1. I can graph rational functions
Lesson 2-5 Part II

2. When graphing a rational function check for:
a) x-intercepts
b) y-intercepts
c) vertical asymptotes
d) horizontal asymptotes
e) holes
f) oblique (slant) asymptotes
g) plot a few extra points if necessary
(make sure that you have the behavior around each asymptote accurate)

3. Graph f(x) = 3/(x – 2)
x-int: none
y-int: (0, -3/2)
VAs: x = 2
HA: y = 0
*How does this graph compare to
f(x) = 1/x?

4. Graph f(x) = (2x + 1)/x
x-int: (-1/2, 0)
y-int: none
VAs: x = 0
HA: y = 2
*Use “long” division to write an equivalent expression for f(x).

5. Graph f(x) = x/(x2 – x – 2)
x-int: (0, 0)
y-int: (0, 0)
VAs: x = -1, x = 2
HA: y = 0

6. Graph f(x) = (2x2 – 18)/(x2 – 4)
x-int: (-3, 0), (3, 0)
y-int: (0, 9/2)
VAs: x = -2, x = 2
HA: y = 2
*Can you explain why this graph would have y-axis symmetry?

7. Graph f(x) = (x+3)/(x2 - 2x)
x-int: (-3, 0)
y-int: none
VAs: x = 0, x = 2
HA: y = 0
After you have graphed this zoom in around x = -3. What do you see?

9. Graph f(x) = (x+3)/(x2+ 5x + 6)
Simplify the expression first.
Graph.
What should you see at x = -3?

10. Let f(x) = (x2 – x )/ (x + 1).
x-int: (0, 0), (1, 0)
y-int: (0, 0)
VAs: x = -1
HA: none
Use long division to write an equivalent expression for f(x). This works when the degree of the numerator is one greater than the degree of the denominator.
We call y = x - 2 a “slant” asymptote.