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Rational Functions (4.6)
Section 3.5 Daily Grade Name ______________________________________________
1. To find a _______________________ asymptote of a rational function in simplest form, set the denominator polynomial equal to zero and solve the equation.
2. To find horizontal asymptotes, compare the degree of the numerator to the degree of the denominator. List the 3 possible cases and the corresponding asymptote.
3. In a rational function, if the degree of the numerator is 1 greater then the degree of the denominator, the graph will have a ________________________________________________.
Circle the correct responses:
4. A graph can cross a (vertical/horizontal) asymptote but can never cross a (vertical/horizontal) asymptote.
SHOW WORK when possible for #5-‐9 Find the vertical asymptote(s) (if any) AND state the domain. Do not graph the function. 5. 𝑓(𝑥) = 2𝑥
2𝑥−3 6. 𝑓(𝑥) = !!!
!!!!"
Find the horizontal asymptotes, if any. Do not graph. If there is no horizontal asymptote, but a slant asymptote exists, find it.
7. 𝑓(𝑥) = 𝑥 2𝑥2−3𝑥+7
8. 𝑓(𝑥) = !! !! !
!!!!!!!!!
9. 𝑓(𝑥) = !
!! !!!!! !!!
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