Q Apply- /(x) = 8 x - 3; < 5 \, | |
Find the range of each function for the given domain. ^ See Problem 4.- /(x ) = 2 * —7; { —2 , - 1 , 0 , 1 , 2 } 19. g(x) = - 4 x + 1; { - 5 , - 1 , 0, 2,10}
- b(x) = x 2; {-1.2, 0, 0.2,1.2, 4}
Find a reasonable domain and range for each function. Then graph the function. ^ See Problem 5.- Fuel A car can travel 32 m i for each gallon of gasoline. The function d[x) = 32x
represents th e distance d(x), in miles, th at th e car can travel with x gallons of
gasoline. The car's fuel tan k holds 17 gal. - Nutrition There are 98 International Units (IUs) of vitam in D in 1 cup of milk. The
function V{c) = 98c represents the a m o u n t V(c) of vitam in D, in IUs, you get from
c cups of milk. You have a 16-cup jug of milk.
Determine whether the relation represented by each table is a function. If the
relation is a function, state the domain and range.- m
Gl ^
(^033) I
- ^
a -4 -1^03
2 1 -1 31 if -4 -4 -4 4 J - Open-Ended Make a table th a t represents a relation th a t is n o t a function. Explain
why the relation is n o t a function. - Reasoning If /(x ) = 6x - 4 a n d f{a) = 26, w hat is th e value of al Explain.
- Think About a Plan In a factory, a certain m ach in e n eeds 10 m in to w arm up. It
takes 15 m in for the m achine to ru n a cycle. The m ach in e can operate for as long
as 6 h p er day including w arm -up time. Draw a graph show ing th e total tim e the
m achine operates d uring 1 day as a function of th e n u m b e r of cycles it runs.
- W hat dom ain an d range are reasonable?
- Is th e function a linear function?
- Carwash A th eate r group is having a carw ash fundraiser. The group can only sp en d
$34 on soap, w hich is enough to w ash 40 cars. Each car is charged $5.
a. If c is th e total n u m b e r of cars w ashed a n d p is the profit, w hich is the
in d e p e n d e n t variable an d w hich is th e d e p e n d e n t variable?
b. Is th e relationship betw een c a n d p a function? Explain.
c. Write an equ atio n th at shows this relationship.
d. Find a reasonable dom ain an d range for th e situation. - Open-Ended W h atv alu e o fx m a k e s th e relation {(1,5), (x, 8), ( - 7 , 9)} afu n ctio n?
Determine whether each relation is a function. Assume that each different
variable has a different value.- {(a, b), (b, a), (c, c), (e, d)} 32. {(b, b), (c, d), {d, c), (c, a)}
- {(c, e), (c, d), (c, b)} 34. {(a, b), (b, c), (c, d), (d, e)}
272 Chapter 4 An Int ro d uct io n t o Funct ions