Chapter 3.5: Graphing Rational Functions
Analyze and graph the function :
(A) The Facts: What do you know?
(i)
What is the Domain of f(x)?
(ii)
What are the Roots (Zeros) of the f(x)?
(iii)
What is the y intercept of f(x)?
(iv)
What happens as x gets very large? What happens when x gets very small?:
As x  ∞ f  x≈
As x −∞ f  x≈
(v)
=
=
“Events” are x values corresponding to x -intercepts or vertical asymptotes.
What are the events for this problem?
x=
Graph the events on the following number line:
Using the graph above as a guide, choose the necessary “test values” for x.
Test values: x =
Determine whether the function is positive or negative in each region using the test
values above:
SHOW YOUR WORK
(B) Interpretation: What do the facts tell you?
(i)
Domain
Vertical Asymptotes:
Graphically this means:
(ii)
Roots
x-intercepts:
Graphically this means:
(iii)
Y-intercept
y intercept:
Graphically this means:
(iv)
Limits
Horizontal Asymptote:
Graphically this means
(v)
Test Points
In what regions is the function always positive?
In what regions is the function always negative?
(C) Graph the Rational Function!
Chapter 3.5: Graphing Rational Functions
Analyze and graph the function :
(A) The Facts: What do you know?
What is the Domain of f(x)?
What are the Roots (Zeros) of the f(x)?
What is the y intercept of f(x)?
What happens as x gets very large? What happens when x gets very small?:
As x  ∞ f  x≈
As x −∞ f  x≈
=
=
“Events” are x values corresponding to x -intercepts or vertical asymptotes.
What are the events for this problem?
x=
Graph the events on the following number line:
Using the graph above as a guide, choose the necessary “test values”for x.
Test values: x =
Determine whether the function is positive or negative in each region using the test values
above:
SHOW YOUR WORK
(B) Interpretation: What do the facts tell you?
Domain
Vertical Asymptotes:
Graphically this means:
Roots
x-intercepts:
Graphically this means:
Y-intercept
y intercept:
Graphically this means:
Limits
Horizontal Asymptote:
Graphically this means
Test Points
In what regions is the function always positive?
In what regions is the function always negative?
(C) Graph the Rational Function!