1. 26 – Limits and Continuity II – Day 2 No Calculator
Rational Function Investigations
26 – Limits and Continuity II – Day 2 No Calculator

2. End Behavior of Rational Functions
If the degree of the numerator is greater than the degree of the denominator, the end behavior will be
If the degree of the numerator is equal to the degree of the denominator, the end behavior will be a horizontal asymptote of f(x) = L
If the degree of the numerator is less than the degree of the denominator, the end behavior will be a horizontal asymptote of f(x) = 0.
Evaluating Infinite Limits of Rational Functions
Select the term with the largest degree in the numerator.
Select the term with the largest degree in the denominator.
Simplify the expression and evaluate the limit.

3. Evaluate each limit below. Determine the end behavior of the function.
Horizontal asymptote:
Horizontal asymptote:
Infinite end behavior
Horizontal asymptote:
Horizontal asymptote:
Infinite end behavior

4. Determine the end behavior of the function.
horizontal asymptote at f(x) = 0.
point discontinuity at (–2, 1)
hole in the graph at (–2, 1)
infinite discontinuity at x = –3
vertical asymptote at x = –3.

5. Determine the end behavior of the function.
horizontal asymptote at g(x) = 0.
point discontinuity
hole at
infinite discontinuity
vertical asymptote at x = –1

6. infinite discontinuity
Determine the end behavior of the function.
horizontal asymptote at h(x) = 1.
point discontinuity
hole at
infinite discontinuity
vertical asymptote
at x = 2

7. Determine the end behavior of the function.
horizontal asymptote at f(x) = 0.
infinite discontinuity
vertical asymptote at x = –4

8. infinite discontinuity at x = 2
Determine the end behavior of the function.
horizontal asymptote at f(x) = 0.
infinite discontinuity at x = 2
vertical asymptote at x = 2

9. Determine the end behavior of the function.
horizontal asymptote at f(x) = 2.
infinite discontinuity
vertical asymptote at x = –1

10. Determine the end behavior of the function.
horizontal asymptote at f(x) = 1.
point discontinuity at x = 3
hole at
infinite discontinuity at x = –1
vertical asymptote at x = –1

11. Determine the end behavior of the function.
horizontal asymptote at f(x) = 2.
point discontinuity at x = –3
hole at
infinite discontinuity at x = 1
vertical asymptote at x = 1