.T h in k ^ _
W h a t is a n o th e r
way to think of the
domain and range?
The domain is the set
of input values for the
function. The range is the
set of output values.
vj Got It? 3. Use the function in Problem 3. How many words can you read in 6 min?
Fi n d i n g t h e Ra n g e o f a Fu n ct i o n
Multiple Choice The domain of f(x) = - 1.5* + 4 is {1,2,3,4}. What is the range?CS> {-2,-0.5, 1,2.5}
C3D {-2 .5 , -1 ,0 .5 , 2}CD {-2 .5 , -1 , -0.5,2}
CD {-2.5, -0.5,1,2}Step 1 Make a table.
List th e d om ain values
as th e x-values.a—1. 5 x + 4 ESI
1 -1.5(1) + 4 2.5
2 -1.5(2) + 4 1(^3) -1.5(3) + 4 -0 .5
4 -1.5(4) + 4 -2
S te p 2 Evaluate f(x)
for each domain value.
The values o f f[x) form
the range.
The range is {-2, -0.5,1,2.5}. T h e c o r r e c t a n s w e r is A.
G o t It? 4. T h e d o m a in o f g ( x ) = 4 x - 12 is { l , 3, 5, 7 }. W h a t is th e ra n g e?
Identifying a Reasonable Domain and Range
Painting You have 3 qt of paint to paint the trim in your house. A quart of paint
covers 100 ft2. The function A(g) = lOOq represents the area A{q), in square feet,
that q quarts of paint cover. What domain and range are reasonable for the function?
What is the graph of the function?
Know ,
' One quart of paint covers
100 ft2.
■ You have 3 qt o f paint.
Reasonable domain
and range values in
order to graph the
function
Find the least and greatest amounts
of paint you can use and areas of
trim you can cover. Use these values
to make a graph.
T h e le a s t a m o u n t o f p a i n t y o u c a n u s e is n o n e. So th e le a s t d o m a in v a lu e is 0. Y o u h a v e
o n ly 3 q t o f p a in t , so th e m o s t p a i n t y o u c a n u s e is 3 q t. T h e g re a te s t d o m a in v a lu e is 3.
The dom ain is 0 < q < 3.
T o f i n d th e ra n g e , e v a lu a te th e f u n c t i o n u s in g th e le a s t a n d g re a te s t d o m a in v a lu e s.
A ( 0 ) = 1 0 0(0) = 0 A ( 3 ) = 1 00(3) = 300
The range is 0 < A(q) < 300.
To graph the function, m ake a table of
v a lu e s. C h o o s e v a lu e s o f q t h a t a re i n th e
d o m a in. T h e g r a p h is a lin e s e g m e n t t h a t
extends from (0, 0) to (3, 300).
Paint Usage
2 2 0 0
3 3 0 0
o- 500
400
,f^300
ru<D^200
<^100
0
I
" |
U,^3 00)
I
1 2 3
Paint Used (qt), q
270 Chapter 4 An Introduction to Functions