Algebra II
Graphing Inverse Variations
Date:________________
Notes 9.2
Objective: To graph inverse variations and translations of inverse variations.
Vocabulary and Key Concepts
k
k
The graph of y 
 c is a translation of y  by b units horizontally and c
x
x b
units vertically. The vertical asymptote is x = b. The horizontal asymptote is y = c.
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. Name the vertices foci, and asymptotes.
16
10
EX 1: y 
EX 2: y 
x
x
2
3
x
EX 4: y 
1
4
x3
8
6
x5
EX 6: y 
2
1
x3
EX 3: y  
EX 5: y 
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
c
x b
y
7
7
 4 so y 
4
x8
x 8
EX 7: Write an equation for the translation of y 
2
that has the asymptotes
x
x = -2 and y = 3.
Write each equation in the form y 
EX 8: y 
1
2x
k
.
x
EX 9: y 
25
3x
EX 10: 3xy  12