1. of the graph of a rational function are the points of intersection of its graph and an axis. of a function are the values of x which make the function of the graph of the 2. zero. The numbered zeroes are also function. 3. of the graph of a rational function r(x), if it exists, occurs at the zeros of the numerator that are not zeros of the denominators. To find equate the function to
1. of the graph of a rational function are the points of intersection of its graph and an axis. of a function are the values of x which make the function of the graph of the 2. zero. The numbered zeroes are also function. 3. of the graph of a rational function r(x), if it exists, occurs at the zeros of the numerator that are not zeros of the denominators. To find equate the function to
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.5: Graphing Rational Functions
Problem 42PS
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Fill in the blanks. Complete the following.
( Intercepts, Zeroes and Asymptotes of Rational Functions )
Transcribed Image Text:1.
of the graph of a rational function are the points of
intersection of its graph and an axis.
2.
of a function are the values of x which make the function
The numbered zeroes are also
of the graph of the
zero.
function.
3.
of the graph of a rational function r(x), if it exists, occurs
at the zeros of the numerator that are not zeros of the denominators. To
find
equate the function to
of the graph of a rational function r(x) if it exists, occurs
simply
4.
at r(0), provided that r(x) is defined at x = 0. To find
evaluate the function at x =
5. An
is an imaginary line to which a graph gets closer and
closer as the x or y increases or decreases its value without limit.
6. То find
of a rational function, first reduce the given
function to simplest form then find the zeroes of the denominator that are
not zeros of the numerator.
of a rational function, compare the degree
7. To determine the
of the numerator n and the degree of the denominator d.
If n < d, the horizontal asymptote is
If n = d, the horizontal asymptote y is the ratio of the leading
coefficient of the numerator a, to the leading coefficient of the
denominator b. That is y =
If n > d, there is
horizontal asymptote.
8. An oblique asymptote is a line that is
oblique asymptote, divide the numerator by the denominator by either
using long division or synthetic division. The oblique asymptote is the
quotient with the remainder ignored and set equal to y.
To determine
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