Section 8.2 – Rational Functions and their Graphs Objectives oIdentify and evaluate rational functions. oGraph a rational function, find its domain, write equations for its asymptotes, and identify any holes in the graph. Warm – Up

What is a rational expression? oA rational expression is the quotient of two polynomials. oA rational function is a function defined by a rational expression. oAn example is

How do you find the domain of a rational function? oThe domain is all real numbers except for where the denominator is zero. oExample…

Example… oWhat is the domain of

How do I find vertical asymptotes and holes of a rational function? oIf a factor is in the denominator of a rational function but not in the numerator of a rational function, then it is a vertical asymptote of the graph of the function. (Non-removable discontinuity) oIf a factor is in both the numerator and the denominator of a rational function, then there is a hole in the graph of the function. (Removable discontinuity)

Example of vertical asymptotes… oFind all the vertical asymptotes of oSet denominator equal to zero. o Solve for x. oWrite equations of vertical asymptotes.

Example with vertical asymptotes and holes. oIdentify all vertical asymptotes and holes in the graph. oREMEMBER: If a factor is in both the numerator and denominator, then it’s a hole. If it is only in the denominator, then it’s a vertical asymptote.

Example… oIdentify all vertical asymptotes and holes in the graph.

What are horizontal asymptotes? oLet, where P and Q are polynomials. oIf the degree of P is less than the degree of Q, then y=0 is the equation of the horizontal asymptote. oIf the degree of P equals the degree of Q and a and b are the leading coefficients of P and Q respectively, then is the equation of the horizontal asymptote. oIf the degree of P is greater than the degree of Q, then the graph has no horizontal asymptotes.

Example of Horizontal Asymptotes… oDetermine horizontal asymptotes (if any).

Exit Slip and Homework oExit Slip is… op. 495 #11-13, oHomework is… op. 495 #14-16, 20-22