11.1

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11.1 Inverse Variation (Please have a
calculator)

• Inverse Variation
• Constant Of Variation

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Definition An Inverse Variation is a function
that can be written in the form
Definition The Constant of Variation k equals
the Product of the quantities (usually x y)
for the described variation.
NOTE! THE GRAPH OF AN INVERSE VARIATION WILL BE
A CURVE, NOT A LINE.
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An Example of Inverse Variation
Suppose Nemo wants to replace his broken iPod. A
new one costs 400 and he will have to work to
earn the money to buy it.
X Values Hourly wage Y Values Number of hours he has to work
5 80
10 40
20 20
50 8
100 4
Constant of Variation
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Comparing Direct and Inverse VariationDirect
variation Inverse Variation- y varies directly
with x - y varies inversely with x- The ratio
y/x is constant - the product (xy) is
constant
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For each table, tell whether y varies inversely
with x. If it does, write a function rule for
the relationship shown by the data.
X Y XY
1 4
3 12
5 20
X Y XY
1 18
4.5 4
6 3
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Each pair of points is from an Inverse Variation.
Find the missing value.
Remember With Inverse Variation, the product
(xy) is constant
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Your Turn! Decide if each is an Inverse
Variation, Direct Variation, or neither
X Y
3 12
6 6
18 2
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• Sentence Frames
• The graph of an Inverse Variation will always be
• a ______________.
• The _____ represents the Constant of Variation
• in the equation y k/x.
• The ________ of the x and y values of
• an inverse variation is a constant.