8.3 Notes Algebra II
Date: ____________________________
I. Vertical and Horizontal Asymptotes
Reciprocal
Function
Parent function: f (x) 
1
x
Create a table of values:
x
f(x)
-3
-2
-1
0
1
2
3
Type of graph: hyperbola
Domain (*limited to values where function is DEFINED):
Range:
Asymptotes:
Intercepts:
Even or odd?
Not defined:
Ex. 1 Limitations on Domain
Determine the value(s) of x for which f(x) is not defined.
a) f (x) 
3
2x  5
b) f (x) 
2
x  5x  24
2
Ex. 2 Properties of Rational Functions
f (x) 
3
x2
Asymptotes:
Domain:
Range:
f (x) 
1
1
x2
Asymptotes:
Domain:
Range:
II. Transformations of Reciprocal Functions
Parent function: f (x) 
h-Horizontal Translation
a-Orientation and Shape
a
k
xh
k-Vertical Translation
Ex. 3 Graph Transformations
Graph each function. State the domain and range.
f (x)  
1
3
x 1
x
f(x)
-3
-2
-1
0
1
2
3
Domain:
Range:
f (x) 
x
-3
-2
-1
0
1
2
3
Domain:
Range:
4
1
x2
f(x)
Ex. 4 Writing Equations
a) Virgin Airlines has a daily non-stop flight between Los Angeles, California, and Sydney, Australia. A one-way trip is
about 7500 miles.
i) Write an equation to represent the travel time from Los Angeles to Sydney as a
function of flight speed. Then graph the equation.
ii) Explain any limitations to the range or domain in this situation.
b) A commuter train has a non-stop service from San Francisco to Belmont, a distance of about 25 miles.
i) Write an equation to represent the travel time between these two cities as a function of rail speed. Then graph
the equation.
ii) Explain any limitations to the range or domain in this situation.
Assignment: p. 548 #1-11 odd, 25, 29, 49, 51, 57