1. 26 – Limits and Continuity II – Day 1 No Calculator
Rational Function Investigations
26 – Limits and Continuity II – Day 1 No Calculator

2. Limit – the intended height of a function
continuous at x = –4
point discontinuity at x = 0
jump discontinuity at x = 2

3. infinite discontinuity at x = –3
When does this happen algebraically?

4. A denominator can never be zero. Therefore….
Rational Function – A quotient of polynomials such that the denominator has a degree of at least 1.
A denominator can never be zero. Therefore….
f(x) is discontinuous at x = –2 and x = –3
g(x) is discontinuous at x = –1 and x = –3
h(x) is discontinuous at x = 2 and x = –1
What type of discontinuity exists?

5. f(x) is discontinuous at x = –2 and x = –3
Any limit resulting in
indicates a point discontinuity.
f(x) is discontinuous at x = –2 and x = –3
There is a point discontinuity at (–2, 1).
There is a hole in the graph at (–2, 1).

6. f(x) is discontinuous at x = –2 and x = –3
Any limit resulting in
indicates an infinite discontinuity.
There is a vertical asymptote in the graph at x = –3.
To determine the behavior of the graph, we substitute values close to x = –3 on each side.
f(x) is discontinuous at x = –2 and x = –3

7. infinite discontinuity point discontinuity vertical asymptote
at x = –1
hole at
g(x) is discontinuous at x = –1 and x = –3

8. infinite discontinuity point discontinuity vertical asymptote at x = 2
hole at
h(x) is discontinuous at x = 2 and x = –1

9. infinite discontinuity at x = –4
9. Determine where
is discontinuous.
Find the type of each discontinuity.
infinite discontinuity at x = –4
vertical asymptote at x = –4
Behavior of graph…..

10. infinite discontinuity at x = 2
10. Determine where
is discontinuous.
Find the type of each discontinuity.
infinite discontinuity at x = 2
vertical asymptote at x = 2
Behavior of graph…..

11. infinite discontinuity
11. Determine where
is discontinuous.
Find the type of each discontinuity.
infinite discontinuity
vertical asymptote at x = –1
Behavior of graph…..

12. Find the type of each discontinuity.
12. Determine where
is discontinuous.
Find the type of each discontinuity.
point discontinuity at x = 3
infinite discontinuity at x = –1
vertical asymptote at x = –1
hole at

13. Find the type of each discontinuity.
13. Determine where
is discontinuous.
Find the type of each discontinuity.
point discontinuity at x = –3
infinite discontinuity at x = 1
vertical asymptote at x = 1
hole at