Quick Review
When the product of two
variables is constant, the
variables form an inverse
variation. You can write an
inverse variation in the form
xy = k o iy = x,k where k is
the constant of variation.Ex a m p l e
Supposey varies inversely with x, and y = 8 whenx = 6.
What is an equation for the inverse variation?
xy = k General form of an inverse variation
6 ( 8 ) = k Substitute 6 forx and 8 fory.
48 = k Simplify.
xy = 48 Write an equation.Ex e r c i se s
Suppose y varies inversely with x. Write an equation for
the inverse variation.- y = 7 when x = 3 28. y = 4 when x = 2.5
- y = - 9 when x = 2 30. y = 5 when x = -5
Graph each inverse variation.
31.xy= l5 32. y = -y^- Running Suppose a runner takes 45 min to run a
route at 8 mi/h at the beginning of training season.
By the end of training season, she can run the same
route in 38 min. What is her speed at the end of
training season?
11 - 6 I n v er se V a r i a t i o n
11 - 7 Gr a p h i n g Rat i o n a l Fu n ct i o n s
Quick Review
A rational function can be written in the form
fix) = The 8raPh of a rational function in the
form y = + c has a vertical asymptote at x = b and a
horizontal asymptote at y = c. A line is an asym pt o t e of a
graph if the graph gets closer to the line as x or y gets larger
in absolute value.Ex a m p l e
What is the graph of /(x) = x f t + 2?
From the form of the function,
you can see that there is a
vertical asymptote at x = 1 and
a horizontal asymptote at y = 2.
Sketch the asymptotes.
Make a table of values. Thena
D-4 -3 -1 0 (^231)
1.8 1.75 1.5 1 3 2.5 1
A
Ex e r c i se s
Identify the excluded value for each function.
- f[x) = | 35. y =x + 4
Identify the asymptotes of the graph of each function.
Then graph the function.36- y= 7T-x + 2 37./W -F&39./M -jA5-1- Physics For a 225-watt bulb, the intensity opr I of light in
lumens at a distance of x feet is / =
a. What is the intensity of light 5 ft from the bulb?
b. Suppose your distance from the bulb doubles.
How does the intensity of the light change?
Explain.
718 Ch a p t er 11 Ch ap t er Rev i ew