2.12. Sign Test for Rational Function Graphs 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
- Identify the vertical asymptotes and use the sign testing procedure to roughly sketch the nature of the function
near the vertical asymptotes.
f(x) =(x−( 3 x)− (^3) x^14 .(^01 x−) 1 ) 2
- Create a function with three vertical asymptotes such that the function approaches negative infinity for large and
small values ofxand has an oblique asymptote. - Identify the vertical asymptotes and use the sign testing procedure to roughly sketch the nature of the function
near the vertical asymptotes.
f(x) =(x−^2 )(^3) (x− 1 ) (^2) (x+ 1 )(x+ 3 )
x^3 (x+^12 )(x− 1 )(x− 2 )^2
Answers:
- The vertical asymptotes occur atx= 0 , 1 ,3.