Unit 3 Review Rational Functions Topics Covered Graphing

Unit 3 Review Rational Functions

Topics Covered • Graphing Rational expressions • Focus was on behaviour – End Behaviour – Asymptotic behaviour from both directions – Test values as x x+ and as x x- for horizontal asymptotes

Be able to… • • Factor and simplify (again) Find x-intercepts (set y=0 and solve) Find y-intercept (set x=0 and solve) Determine vertical asymptotes – Factor denominator and set factors equal to 0

Horizontal Asymptotes – If , then y=0 – If , then Where “a” and “b” are leading coefficients

Oblique Asymptotes If degree in numerator > degree in denominator Then an oblique asymptote exists. Oblique asymptote will be

Holes in Function • Holes in functions occur when we cancel out factors in our equations • Steps: – Factor – Simplify, but make note of where “hole” is – Graph resulting function – Find point by substituting x-value where hole exists into new equation

Also • Solve algebraically – Used to find points of intersection • Inequalities between two functions – Graph both functions – Find points of intersection – Determine intervals where inequality is satisfied

Complete the chart below for the function

Graph the function .

Write an equation of a function that has all of the following properties. § § § Vertical asymptotes at x=7 and x=-2. Horizontal asymptote at y=0. Two x-intercepts at 1 and 5.

Textbook Review and more! • Pg. 480 #17, 18(i, iii), 20, 21