2.13. Graphs of Rational Functions by Hand http://www.ck12.org
Vocabulary
Thesign testis a procedure for determining only whether a function is above or below thexaxis at a particularx
value. The specific height is not calculated.
Oblique asymptotesare asymptotes that occur at a slant. They are always lines.
Ahorizontal asymptoteis a flat dotted line that indicates where a function goes asxget infinitely large or infinitely
small.
End behavioris a term that asks you to describe the horizontal asymptotes.
Avertical asymptoteis a dashed vertical line that indicates that as a function approaches, it shoots off to positive or
negative infinity without ever actually touching the line.
Arational functionis a function with at least one rational expression.
Arational expressionis a ratio of two polynomial expressions.
Guided Practice
- Graph the following rational function:
f(x) =x (^2) + 31 x+ 2
- Graph the following rational function:
f(x) = −x4
10 (x− 1 )^2 (x− 2 )^2 (x− 4 )^2- Graph the following rational function:
f(x) =^3 x(^3) + 4 x− 2 x− 4
x^2 − 7 x+ 12
Answers:
- Here is the graph:
- Here is the graph: