February 24, 2016
8.3 Rational Functions and Their Graphs
Reciprocal function
examples:
Rational function
February 24, 2016
Here are graphs of 3 rational
functions:
continuous graph
-no breaks or
holes
discontinuous graph
-has a hole
Your calculator only
shows holes in the table
of values, not the graph.
discontinuous graph
-has a vertical
asymptote
Your calculator
shows vertical asymptotes in
the table and the graph.
February 24, 2016
Does the graph have a hole
or a vertical asymptote?
but (x+2) cancels out. A hole is created at
x=-2. It is removable discontinuity.
but x+2 does not cancel. A Vertical Asymptote is
created at x=-2. It is non-removable discontinuity.
February 24, 2016
Find the domain, points of discontinuity(P of D) and x- and yintercepts for each rational function. Are the discontinuities
removable(holes) or non-removable(vertical asymptote)?
1.
2.
Domain: ________________
All Real numbers
Domain: ________________
P of D __________________
None
P of D __________________
Non-removeable
Vertical Asymptote
Type? ____________________
N/A
Type? ____________________
x-intercept: ________________
Let y=0
x-intercept: ________________
Let y=0
none
y- intercept: _______________
Let x=0
y- intercept: _______________
Let x=0
February 24, 2016
Find the domain, points of discontinuity and x- and yintercepts for each rational function. Are the discontinuities
removable(holes) or non-removable(vertical asymptote) ?
3.
Domain: ________________
P of D __________________
removeable non-removeable
vertical asymptote
Type? ____________________
hole
none
x-intercept: ________________
Let y=0
y- intercept: _______________
Let x=0
4.
Domain: ________________
P of D __________________
removeable
Type? ____________________
hole
x-intercept: ________________
Let y=0
y- intercept: _______________
Let x=0
February 24, 2016
Find the domain, points of discontinuity and x- and yintercepts for each rational function. Are the discontinuities
removable(holes) or non-removable(vertical asymptote) ?
5.
Domain: ________________
P of D __________________
non-removeable
vertical asymptotes
Type? ____________________
x-intercept: ________________
Let y=0
y- intercept: _______________
Let x=0
6.
Domain: ________________
P of D __________________
non-removeable
vertical asymptotes
Type? ____________________
none
x-intercept: ________________
Let y=0
y- intercept: _______________
Let x=0
February 24, 2016
February 24, 2016
Find the domain, points of discontinuity and x- and yintercepts for each rational function. Are the discontinuities
removable(holes) or non-removable(vertical asymptote) ?
7.
Domain: ________________
P of D __________________
removeable non-removeable
hole
vertical asymptote
Type? ____________________
none
x-intercept: ________________
Let y=0
y- intercept: _______________
Let x=0
8.
Domain: ________________
P of D __________________
non-removeable
removeable
vertical asymptote
hole
Type? ____________________
x-intercept: ________________
Let y=0
y- intercept: _______________
Let x=0
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February 24, 2016
HW p. 521; 1 - 8 all, 13 - 21 all
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