I can graph rational functions Lesson 2-5 Part II

When graphing a rational function check for: a) x-intercepts b) y-intercepts c) vertical asymptotes d) horizontal asymptotes e) holes f) oblique (slant) asymptotes g) plot a few extra points if necessary (make sure that you have the behavior around each asymptote accurate)

Graph f(x) = 3/(x – 2) x-int: none y-int: (0, -3/2) VAs: x = 2 HA: y = 0 *How does this graph compare to f(x) = 1/x?

Graph f(x) = (2x + 1)/x x-int: (-1/2, 0) y-int: none VAs: x = 0 HA: y = 2 *Use “long” division to write an equivalent expression for f(x).

Graph f(x) = x/(x2 – x – 2) x-int: (0, 0) y-int: (0, 0) VAs: x = -1, x = 2 HA: y = 0

Graph f(x) = (2x2 – 18)/(x2 – 4) x-int: (-3, 0), (3, 0) y-int: (0, 9/2) VAs: x = -2, x = 2 HA: y = 2 *Can you explain why this graph would have y-axis symmetry?

Graph f(x) = (x+3)/(x2 - 2x) x-int: (-3, 0) y-int: none VAs: x = 0, x = 2 HA: y = 0 After you have graphed this zoom in around x = -3. What do you see?

Graph f(x) = (x+3)/(x2+ 5x + 6) Simplify the expression first. Graph. What should you see at x = -3?

Let f(x) = (x2 – x )/ (x + 1). x-int: (0, 0), (1, 0) y-int: (0, 0) VAs: x = -1 HA: none Use long division to write an equivalent expression for f(x). This works when the degree of the numerator is one greater than the degree of the denominator. We call y = x - 2 a “slant” asymptote.