Math 233A Homework 12: Functions and Their Properties, Exercises of Algebra

Math 233a homework 12, focusing on chapter 3.2: functions. Students are required to determine if given relations are functions, estimate their domains, ranges, and find function values. Additionally, they need to simplify functions using specific values and analyze the behavior of certain functions.

Typology: Exercises

2012/2013

Uploaded on 01/07/2013

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Math
233A
Homework #12
Chapter 3.2: Functions
1. Use the vertical line
test
to
determine
whether
each
relation is a function, and if so,
estimate
the
domain,
range,
and /(0); if not a function
state
n/a.
(a)
b
/\
Function?
(b)
Function?
(c)
> ]
Function?
Name
2.
Simplify
the function using each indicated
value:
a. Find/(0).
b.
Find/(-2).
Domain: Domain: Domain:
Range: Range: Range:
c. Fmd/(-3),
/(0) = /(0) = /(0) =
d.
Find/(a)
3. The function V{N) = 18500 -15007/ predicts the value, V(N), in dollars, of a car
//years
after
the
purchase.
a.
Find
V(0)...
What
does
this
tell
us?
b.
Find
F(20)... What
does
this
make
sense?
Why?
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Math 233A Homework # Chapter 3.2: Functions

  1. Use the vertical line test to determine whether each relation is a function, and i f so, estimate the domain, range, and / ( 0 ) ; i f not a function state n/a.

(a)

b

/\

Function?

(b)

Function?

(c)

]

Function?

Name

  1. Simplify the function using each indicated value:

a. F i n d / ( 0 ).

b. F i n d / ( - 2 ).

Domain: Domain: Domain:

Range: Range:^ Range:

c. F m d / ( - 3 ) ,

d. F i n d / ( a )

  1. The function V{N) = 18500 -15007/ predicts the value, V(N) , in dollars, o f a car //years after the purchase.

a. Find V(0)... What does this tell us?

b. Find F(20)... What does this make sense? Why?

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c. Solve the equation V(N)=500... What does this tell us?

d. Find the domain and range o f this function.

  1. The function P(T) = (60 + 97) ^ (10 + 0.67) predicts the global population, P(T) , i n billions, after the

year 2000.

a. Find P{0)... What does this tell us?

b. F m d P{50)... What does this tell us?

c. Find /*(100)... What does the pattern i n these numbers suggest? What can we say about the rate at which the population increases?

d. If the domain for this function is 0 < 7 < 100, then what is the range o f this function?

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