Algebra II
Graphing Inverse Variations
Date:________________
Notes 8.2
Objective: To graph inverse variations and translations of inverse variations.
Vocabulary and Key Concepts
The general form of a member of the reciprocal function family is y 
a
k.
x h
|a| > 1
Stretch
0 < |a| < 1
Shrink
a<0
Reflection
h
Translation h units left or right
Vertical asymptote: x = h
k
Translation k units up or down
Horizontal asymptote: y = k
A branch is each piece of a discontinuous graph.
We will not make a table of values from scratch. We will use our calculators to
produce a table, plot points and connect.
Graph the following. Sketch the asymptotes and name the domain and range.
10
1
EX 1: y 
EX 2: y 
4
x
x3
EX 3: y  
2
3
x
EX 4: y 
2
1
x3
Writing the Equation of a Translation
Write an equation for the translation of y  
7
that has asymptotes at
x
x = 8 and y = - 4.
Answer:
y
7
7
7
 k plug in h and k so y 
4
 4 so y 
x h
x8
x 8
EX 5: Write an equation for the translation of y 
2
that has the asymptotes
x
x = -2 and y = 3.
Graph each pair of functions. Find the approximate point(s) of intersection.
6
EX 6: y 
;y=6
x2