CH 5.3 Graph General Rational Functions.notebook AWS
CH 5.3 Graph General Rational Functions.notebook
Graph Rational Functions 5.3 Graph General Rational Functions • Graphs • Asymptotes • Using graphs to problem solve
Jan 234:08 PM
Graph Simple Rational Functions
January 24, 2013
Graph Simple Rational Functions Finding Horizontal Asymptotes with a Rational Function
If the degree of the numerator is equal to the degree of the denominator, then the horizontal asymptote of the rational function is the ratio of the leading coefficients.
Jan 2112:40 PM
Graph Simple Rational Functions Finding Horizontal Asymptotes with a Rational Function If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote of the rational function x=0.
Jan 2112:40 PM
Graph Simple Rational Functions
Jan 2112:40 PM
Graph Simple Rational Functions Finding Horizontal Asymptotes with a Rational Function If the degree of the numerator is greater than the degree of the denominator, then the horizontal asymptote of the rational function does not exist.
Jan 2112:40 PM
Jan 2112:40 PM
1
CH 5.3 Graph General Rational Functions.notebook
Graph Simple Rational Functions
January 24, 2013
Graph Simple Rational Functions
Vertical Asymptote
Jan 2112:40 PM
Graph Simple Rational Functions
Horizontal Asymptote
Jan 2112:40 PM
Graph Simple Rational Functions
Vertical Asymptotes
Horizontal Asymptotes
Jan 2112:40 PM
Graph Simple Rational Functions
Jan 2112:40 PM
Graph Rational Functions After finding the vertical and horizontal asymptotes, we need to find the places where the function crosses the xaxis. We will need to find the zeros of the numerator.
Jan 2112:40 PM
Jan 234:08 PM
2
CH 5.3 Graph General Rational Functions.notebook
Graph Rational Functions Find the intercepts asymptotes and the domain of the function.
Jan 234:08 PM
Graph Rational Functions Factor the denominator to find the vertical asymptotes.
January 24, 2013
Graph Rational Functions Factor the numerator to find the intercepts.
Jan 234:08 PM
Graph Rational Functions
Once we find the vertical asymptotes, we know the domain.
Vertical Asymptotes
Domain: All real numbers except, x=1 and x=1
Jan 234:08 PM
Graph Rational Functions
Jan 234:08 PM
Graph Rational Functions
Find the intercepts asymptotes and the domain of the function.
Jan 234:08 PM
Jan 234:08 PM
3
CH 5.3 Graph General Rational Functions.notebook
Graph Rational Functions Factor the numerator to find the intercepts.
Jan 234:08 PM
Graph Rational Functions
January 24, 2013
Graph Rational Functions Factor the denominator to find the vertical asymptotes.
Jan 234:08 PM
Graph Rational Functions
Once we find the vertical asymptotes, we know the domain. Vertical Asymptotes
Domain: All real numbers except, x=0 and x=3
Jan 234:08 PM
Jan 234:08 PM
Graph Rational Functions 5.3 Graph General Rational Functions • Graphs • Asymptotes • Using graphs to problem solve
Jan 234:08 PM
4
Graph Rational Functions 5.3 Graph General Rational Functions • Graphs • Asymptotes • Using graphs to problem solve
Jan 234:08 PM
Graph Simple Rational Functions
January 24, 2013
Graph Simple Rational Functions Finding Horizontal Asymptotes with a Rational Function
If the degree of the numerator is equal to the degree of the denominator, then the horizontal asymptote of the rational function is the ratio of the leading coefficients.
Jan 2112:40 PM
Graph Simple Rational Functions Finding Horizontal Asymptotes with a Rational Function If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote of the rational function x=0.
Jan 2112:40 PM
Graph Simple Rational Functions
Jan 2112:40 PM
Graph Simple Rational Functions Finding Horizontal Asymptotes with a Rational Function If the degree of the numerator is greater than the degree of the denominator, then the horizontal asymptote of the rational function does not exist.
Jan 2112:40 PM
Jan 2112:40 PM
1
CH 5.3 Graph General Rational Functions.notebook
Graph Simple Rational Functions
January 24, 2013
Graph Simple Rational Functions
Vertical Asymptote
Jan 2112:40 PM
Graph Simple Rational Functions
Horizontal Asymptote
Jan 2112:40 PM
Graph Simple Rational Functions
Vertical Asymptotes
Horizontal Asymptotes
Jan 2112:40 PM
Graph Simple Rational Functions
Jan 2112:40 PM
Graph Rational Functions After finding the vertical and horizontal asymptotes, we need to find the places where the function crosses the xaxis. We will need to find the zeros of the numerator.
Jan 2112:40 PM
Jan 234:08 PM
2
CH 5.3 Graph General Rational Functions.notebook
Graph Rational Functions Find the intercepts asymptotes and the domain of the function.
Jan 234:08 PM
Graph Rational Functions Factor the denominator to find the vertical asymptotes.
January 24, 2013
Graph Rational Functions Factor the numerator to find the intercepts.
Jan 234:08 PM
Graph Rational Functions
Once we find the vertical asymptotes, we know the domain.
Vertical Asymptotes
Domain: All real numbers except, x=1 and x=1
Jan 234:08 PM
Graph Rational Functions
Jan 234:08 PM
Graph Rational Functions
Find the intercepts asymptotes and the domain of the function.
Jan 234:08 PM
Jan 234:08 PM
3
CH 5.3 Graph General Rational Functions.notebook
Graph Rational Functions Factor the numerator to find the intercepts.
Jan 234:08 PM
Graph Rational Functions
January 24, 2013
Graph Rational Functions Factor the denominator to find the vertical asymptotes.
Jan 234:08 PM
Graph Rational Functions
Once we find the vertical asymptotes, we know the domain. Vertical Asymptotes
Domain: All real numbers except, x=0 and x=3
Jan 234:08 PM
Jan 234:08 PM
Graph Rational Functions 5.3 Graph General Rational Functions • Graphs • Asymptotes • Using graphs to problem solve
Jan 234:08 PM
4
