Objective: Graph rational functions. Identify slant asymptotes

Objective: Graph rational functions.

Warm up1. Find the following:

a.

b.

c.

d.

2. Find the domain and identify the vertical asymptotes and holes.

2

1( )2 3xf x

x x

Vertical Asymptotes: zeros of the denominator. (If there are no common factors for numerator and denominator)

Horizontal Asymptotes: Leading terms

• If n = m;• If m > n; • If m < n; no H.A.

Oblique Asymptotes: when m < n; divide numerator by denominator.

Holes: If there are common factors for numerator and denominators. T At the value of x that makes common factors equal zero.

Example 1Make a table of values to graph . Identify the vertical andand horizontal asymptotes.

Example 2Graph using transformations.

a.

b.

c.

Example 3Graph

a.

b.

Assignments:Gizmo: Rational Functions

Carnegie Learning Marathon: 7.1-7.3

Classwork:Pg 355 #37-48

Slant Asymptotes: Degree of numerator is greater. Divide numerator by denominator. ( y = mx+b form).

Example 3Find the slant asymptotes.

a.

b.

Continuation of previous lesson (10/18/12)

Example 5Sketch the graphs. Include asymptotes, intercepts, tables of values used.

a.

b.