Math Homework 12: Determining Functions, Domains, and Ranges, Exercises of Algebra

Math 23 3a homework #12, focusing on chapter 3.2: functions. Students are required to use the vertical line test to determine if each relation is a function, estimate domains and ranges, and simplify functions using given values. Additionally, they need to find the value of functions for specific inputs and interpret the results.

Typology: Exercises

2012/2013

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Math
23
3A
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)
b
A
-a-
Function? Function?
(c)
\
\
Function?
Domain:
Range:
Domain:
Range:
.AO)
= -(X /(O) =
Domain:
'00<X.<CC
Range:
-QD<X<cc
m
3. The function V{N) = 18500 -1500// predicts the value
purchase.
a.
Find
F(0)... What
does
this
tell
us?
Name
2.
Simplify
the function using each indicated
value:
x'-9
a. Find/(0).
1
b.
Find/(-2).
c. Find/(-3).
d.
Find/(a)
!,
V{N), in dollars, of a car
years
after
the
b.
Find
F(20)... What
does
this
make
sense?
Why? rKt^:>oV
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Math 23 3A 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); if not a function state n/a.

(a) (b)

b

A

-a-

Function? Function?

(c)

\

\

Function?

Domain:

Range:

Domain:

Range:

.AO) = -(X /(O) =

Domain:

'00 <X.<CC

Range:

-QD<X<cc

m

  1. The function V{N) = 18500 -1500// predicts the value purchase.

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

Name

  1. Simplify the function using each indicated value:

x'-

a. Find/(0).

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

c. F i n d / ( - 3 ).

d. Find/(a)

!, V{N) , in dollars, of a car years after the

b. Find F(20)... What does this make sense? Why? rKt^:>oV

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c. Solve the equation F (A0=5OO. .. What does this tell us?

.-mo

~ \ ' ^ - \ ' 5 G C

d. Find the domain and range of this function.^^^^^\X^

m b ^ycaoA ^A

4. The function P(r) = (60 + 97') + (10+0.6r) predicts the global population, ^(7"), in billions, after the

year 2000.

a. FindPCO)... Whatdoesthistellus? V ^lHTtb :>^Vi 'i^ P ^ ^ ^ ^ "

b. Find P(50),.. What does th,s tell us? \7'4-^ Vd^Wv'Cn

c. Find P(IOO)... What does the pattern in these numbers suggest? What can we say about the rate at which the population increases?

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

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