Date post: | 31-Dec-2015 |
Category: |
Documents |
Upload: | archibald-chandler |
View: | 213 times |
Download: | 0 times |
WAIT No quiz on dividing polynomials. Next
assessment is Unit 2 test! Continue to study by reviewing the
vocabulary flash cards you’ve already made, doing the homework from the Wiki, and doing skill and word problems.
Make office hours appointments as needed.
TEST TOPICS Power functions Solve radical functions Polynomial functions
Division Zeros
Rational functions Domain, asymptotes, holes, intercepts
There will be one question from the last unit test.
RATIONAL FUNCTION A rational function is the quotient of two
polynomial functions and , where is nonzero.
The domain of a rational function is all real numbers excluding those values for which , or the zeroes of
RATIONAL FUNCTIONS
The reciprocal function, like many rational functions has parts that approach specific - and -values.
The lines representing those values are called asymptotes.
This is not piecewise.
VERTICAL ASYMPTOTES
Vertical asymptotes can only exist where the domain of a function is discontinuous.
But just because a function is discontinuous at particular value of doesn’t mean it will form an asymptote, so check.
HORIZONTAL ASYMPTOTES Let be a rational function defined as:
and are polynomials with no common factors. Let have degree and have degree The graph may have 1 or 0 horizontal asymptotes
using these guidelines: If , the horizontal asymptote is . If , the horizontal asymptote is If there is no horizontal asymptote.
OBLIQUE/SLANT ASYMPTOTES
We call these oblique or slant asymptotes.
What does oblique mean? It means slanted. These occur when a graph approaches
a linear relationship at its ends.
OBLIQUE/SLANT ASYMPTOTES Let be a rational function defined as:
Where and and have no common factors other than . If , the graph has an oblique asymptote. It’s
determined by dividing the numerator and denominator:
The asymptote will run along the line .
SLANT ASYMPTOTE
We know this has a vertical asymptote at . Because , there are no horizontal
asymptotes. Because , there is a slant asymptote. Do the long division… Slant asymptote at .
is a rational function with the form . Given the information that has zeros at , which of the following MUST be true?
I. has degree 3II. has asymptotes at III. has a domain
a) I onlyb) II onlyc) III onlyd) I and II onlye) I, II, and III
is a rational function with the form . Given the information that has zeros at , which of the following CAN be true?
I. has degree 3II. has asymptotes at III. has a domain
a) I onlyb) II onlyc) III onlyd) I and II onlye) I, II, and III
Given the rational equation , identify the equation of the horizontal asymptote:
a) There is no horizontal asymptote.
a) Given the rational equation , identify the equation of the horizontal asymptote:
b) There is no horizontal asymptote.