Download 9.2 Graphing Simple Rational Functions

9.2
Graphing Simple Rational
Functions
Rational Functions

Rational Function: is a function of
the form
p( x)
f ( x) 
q ( x)
Hyperbola
x
-4
-3
-2
-1

1
2
1
2
1
2
3
4
y
1
f ( x) 
x
Rational Functions

Hyperbola: the graph of a rational
function.




The x-axis is a horizontal asymptote
The y-axis is a vertical asymptote
The domain and range are all nonzero
real numbers
The graph has two symmetrical parts
(branches)
Investigation
1)
Graph each function.
2
x
c)
3
y

b)
x
d)
a)
2)
3)
y
y
y
1
x
2
x
Use the graphs to describe how the
a
sign of a affects the graph of y  x .
Use the graphs to describe how a
affects the graph of y  a .
x
Rational Functions (In General)

Rational Functions in the form…
a
y
k
xh

Asymptotes are at…
x = h and y = k
Examples: Graph the functions
and state the domain and range.
1)
2)
3)
3
y
2
x 1
x2
y
3x  3
1
y
3
x4
Examples:
4)
The senior class is sponsoring a
dinner. The cost of catering the
dinner is $9.95 per person plus an
$18 delivery charge.
a)
b)
Write a model that gives the average
cost per person.
Graph the model and use it to
estimate the number of people needed
to lower the cost of $11 per person.
Example (Continue):
c)
Describe what happens to the average
cost per person as the number
increases.
Example:
4)
The speed of sound can be
modeled by 1.09F + 1087.8 ft/sec,
where F is the temperature in oF.
a)
b)
Write a model that gives the time it
takes you to hear thunder a mile
away.
Graph the model and use it to
estimate to how long it takes you to
hear the thunder a mile away if it is
75o.
Example (Continue)
c)
Describe what happens to the length
of time it takes for the thunder to
reach your ears as the temperature
decreases.