Chapter 9 Additional Functions Topics Worksheet - Mcgraw-Hill Higher Education printable pdf download

Chapter 9 Additional Functions Topics Worksheet - Mcgraw-Hill Higher Education

510

(9-20)

Chapter 9 Additional Function Topics

V A R I A T I O N

9.3

If y

3x, then as x varies so does y. Certain functions are customarily expressed

I n t h i s

in terms of variation. In this section you will learn to write formulas for those

s e c t i o n

functions from verbal descriptions of the functions.

Direct Variation

Finding the Proportionality

Constant

In a community with an 8% sales tax rate, the amount of tax, t (in dollars), is a

Inverse Variation

function of the amount of the purchase, a (in dollars). This function is expressed by

the formula

Joint Variation

More Variation

0.08a.

If the amount increases, then the tax increases. If a decreases, then t decreases.

In this situation we say that t varies directly with a, or t is directly proportional to a.

The constant tax rate, 0.08, is called the variation constant or proportionality

constant. Notice that t is just a simple linear function of a. We are merely introduc-

ing some new terms to express an old idea.

Direct Variation

The statement y varies directly as x, or y is directly proportional to x,

means that

for some constant, k. The constant, k, is a ﬁxed nonzero real number.

Finding the Proportionality Constant

If y varies directly as x and we know corresponding values for x and y, then we can

ﬁnd the proportionality constant.

E X A M P L E

Finding the proportionality constant

Joyce is traveling by car, and the distance she travels, d, varies directly with

c a l c u l a t o r

the amount of time, t, that she drives. In 3 hours she drove 120 miles. Find the

proportionality constant and write d as a function of t.

c l o s e - u p

Solution

Because d varies directly as t, we must have a constant k such that

The graph of d

40t is a

straight line through the

kt.

origin.

240

Because d

120 when t

3, we can write

120

k 3,

So the proportionality constant is 40 mph, and d

40t.

Chapter 9 Additional Functions Topics Worksheet - Mcgraw-Hill Higher Education

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