Rational Expressions GRAPHING.

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Presentation transcript:

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

Domain: (-∞,-5) U (-5,1) U (1,∞) Vertical Asymptote(s) x=1 & x=-5 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

H.A.  y = 0 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

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

Find y-intercept Substitute zero for x and find the value of the function

Sketch the graph Vertical Asymptotes Horizontal Asymptote y-intercept Plot a few points x y -10 .05 -5.5 .92 -4.5 -1.1 .5 1.5 10 .02

Domain: (-∞,-6) U (-6,-1) U (-1,∞) Vertical Asymptote(s) x=-1 4 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

H.A.  y = the ratio of the lead coefficients. 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 Substitute zero for x and find the value of the function

Sketch the graph Vertical Asymptote Point of Discontinuity Horizontal Asymptote y-intercept Plot a few points x y -10 1.8 -2 8 -.5 -13 1 -2.5 10 .4

Vertical Asymptote(s) NONE Find Point of Discontinuity at -4 6 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

H.A.  there is no horizontal asymptote 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

Find y-intercept Substitute zero for x and find the value of the function

Sketch the graph Point of Discontinuity y-intercept Plot a few points x y -5 -9 -3 -7 4

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.

Homework – day 2 Page 405 21-43 odd