Transcript graphing rational expressions
Rational Expressions
GRAPHING
Objectives
Graph a rational function, find its domain, write equations for its asymptotes, and identify any holes (point discontinuity) in its graph.
Glossary Terms
asymptote horizontal asymptote point discontinuity rational function vertical asymptote y-intercept
Rational Function
An equation in the form Where p(x) and q(x) are polynomial functions and q(x) 0.
When graphing rational functions
State domain Find Vertical Asymptote(s) Find Point of Discontinuity in the graph (HOLES) Find Horizontal Asymptote Find the y-intercepts & x-intercepts Sketch
3
State Domain Find Vertical Asymptote(s) Find Point of Discontinuity in the graph Domain: ( ∞,-5) U (-5,1) U (1,∞) Vertical Asymptote(s) x=1 & x=-5 Find Point of Discontinuity in the graph - none
3
Find Horizontal Asymptote Compare the degree of the numerator to the degree of the denominator degree of the numerator < degree of the denominator H.A. y = 0
3
Find Horizontal Asymptote Compare the degree of the numerator to the degree of the denominator degree of the numerator < degree of the denominator H.A. y = 0 degree of the numerator = degree of the denominator H.A. y = the ratio of the lead coefficients.
degree of the numerator > degree of the denominator none
3
Find y-intercept Substitute zero for x and find the value of the function
3
3 5
Sketch the graph
Vertical Asymptotes Horizontal Asymptote y-intercept Plot a few points x -10 -5.5
-4.5
.5
1.5
10 .05
y .92
-1.1
-1.1
.92
.02
3
4
x 2 x 2
36
State the domain Find Vertical Asymptote(s) Find Point of Discontinuity in the graph Domain: ( ∞,-6) U (-6,-1) U (-1,∞) Vertical Asymptote(s) x=-1 Find Point of Discontinuity at -6
x 2 x 2
36
Find Horizontal Asymptote Compare the degree of the numerator to the degree of the denominator degree of the numerator = degree of the denominator H.A. y = the ratio of the lead coefficients.
y = 1
Find y-intercept
x 2 x 2
36
Substitute zero for x and find the value of the function
0 2
6
36 6
6
Sketch the graph
Vertical Asymptote Point of Discontinuity Horizontal Asymptote y-intercept Plot a few points x -10 -2 -.5
1 10 1.8
y 8 -13 -2.5
.4
x 2 x 2
36
6
x 2
16
State the Domain Find Vertical Asymptote(s) Find Point of Discontinuity in the graph Domain: ( ∞,-4) U (-4,∞) Vertical Asymptote(s) NONE Find Point of Discontinuity at -4
x 2
16
Find Horizontal Asymptote Compare the degree of the numerator to the degree of the denominator degree of the numerator > degree of the denominator H.A. there is no horizontal asymptote
x 2
16
Find y-intercept Substitute zero for x and find the value of the function
0
4
16 4
4
Sketch the graph
Point of Discontinuity y-intercept Plot a few points -5 x -3 4 -9 -7 0 y
x 2
16
Homework – day 1
Rational Functions Worksheet 1, part A & B Graphing Rational Function Worksheet #1-3, 5
Graphing Rational Expressions Oblique Asymptotes
To find Oblique (Slant) Asymptotes you will need to divide.
x
2
x
9
x
3 20 3
x
3 2
x x
2 2 1 3
x
4
Homework – day 2
Page 405 21-43 odd