Class Notes (808,045)
Mathematics (837)
MATA30H3 (41)
Lecture

rational functions.docx

2 Pages
108 Views

School
University of Toronto Scarborough
Department
Mathematics
Course
MATA30H3
Professor
Ken Butler
Semester
Winter

Description
Reciprocal of a Linear Function  The reciprocal of a linear function has the form: f(x) = 1 / kx – c  The restriction on a domain of a reciprocal linear function can be determined by finding the value of x that makes the denominator equal to zero, that is x = c / k.  The Vertical Asymptote of a reciprocal linear function has an equation of the form x = k / c.  The horizontal asymptote of a reciprocal linear function has equation y = 0.  If k > 0, the left branch of a reciprocal linear function has a negative, decreasing slope, and the right branch has a negative, increasing slope.  Basically occupies Q3 and Q1.  If k < 0, the left branch of a reciprocal linear function has a positive, increasing slow, and the right branch has a positive, decreasing slope.  Basically occupies Q2 and Q4. Reciprocal of a Quadratic Function  Rational functions can be analyzed using key features: asymptotes,intercepts, slope (positive or negative, increasing or decreasing),domain, range, and positive and negative intervals.  Reciprocal of quadratic functions with two zeros have three parts, with the middle one reaching a maximum or minimum points. This point is equidistant from the two vertical asymptotes.  The behavior near asymptotes is similar to that of reciprocals of linear functions.  All of the behaviors listed above can be predicted by analyzing the roots of the quadratic relation to the denominator. Rational Functions of the form f(x) = (ax + b) / (cx + d)  A rational function of the form f(x) = (ax + b) / (cx + d) has the following key features:  The vertical asymptote can be found by setting the denominator equal to zero and solving for x, provided the numerator does not have the same zero.  The horizontal asymptot
More Less

Related notes for MATA30H3

OR

Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.