OEMAT1033+3
.docx
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School
Florida Technical College, Orlando *
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Course
1033
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
Pages
3
Uploaded by MinisterPanther1621
3.5
Find the Domain and Range of a Relation
For the relation {(1,4), (2,1), (3,-5), (4,-11), (5,-20)}
a.
Determine the domain.
b.
Determine the range.
Determine the domain and range of f(x).
The domain
is the set of all possible inputs (x-values). The range
is the set of all possible outputs (y-values).
Determine if a Relation is a Function
A function
is a relation that assigns to each element in its domain exactly one element in the range.
For the relation: {(-5,3),(-2,7),(0,12),(2,18),(5,25)}
a.
Is the relation a function?
b.
Determine the domain.
c.
Determine the range.
For the relation: {(5,3),(2,7),(0,12),(2,18),(5,25)}
a.
Is the relation a function?
b.
Determine the domain.
c.
Determine the range.
For each equation, determine whether the equation shows y as a function of x.
3
x
+
y
=
14
y
=
x
3
+
5
x
−
y
2
=
9
Select all of the equations for which y is a function of x.
x
+
4
y
=
8
y
=
±x
y
=
5
x
=−
2
Find the Value of a Function
Find the value of each function. f
(
x
)
=
x
2
−
5
x
+
6
f
(
4
)
=
¿
f
(
−
3
)
=
¿
Find the value of each function. g
(
t
)
=−
t
2
+
2
t
−
12
g
(
−
3
)
=
¿
g
(
3
x
)
=
¿
Find the value of each function. h
(
y
)
=
2
y
2
−
y
+
7
h
(
m
−
2
)
=
¿
f
(
x
)
=
3
x
2
−
x
f
(
−
4
)
=
¿
g
(
x
)
=
2
3
x
g
(
−
6
)
=
¿
3.5
T
(
n
)
=
|
n
|
−
2
T
(−
5
)=
¿
k
(
x
)
=
2
x
k
(
3
)=
¿
d
(
r
)
=(
2
r
)
3
d
(−
3
)=
¿
P
(
n
)
=
1
n
2
P
(−
6
)=
¿
Given f
(
x
)
=
2
x
2
−
5
x
+
1
, determine the function values.
f
(
2
)
=
¿
f
(
−
4
)
=
¿
f
(
1
2
)
=
¿
Given f
(
x
)
=−
2
x
2
+
3
x
+
7
, find the function values using your graphing calculator.
f
(
−
1
)
=
¿
f
(
3
4
)
=
¿
Since the last update, the number of users of a website can be modeled by the function N
(
t
)
=
3600
+
45
t ,
where t is measured in days.
a.
Determine the independent and dependent variables.
b.
Find N(0). Explain what this result means.
c.
Find N(10). Explain what this result means.
The function V
(
m
)
represents value of an investment (in thousands of dollars) after m months. Explain the meaning of V
(
24
)=
18
.
Function Notation
f
(
x
)=
y
f
(
input
)=
output
The cost to fill your motorhome’s propane tank is determined by the function C(g)=3.11g, where C(g) is the output (cost in $) and g is the input (gallons of propane). The propane tank can hold a maximum of 12 gallons.
Part A: 1. Calculate C
(
4
)
:
C
(
4
)=
¿
2.
Write your answer as an ordered pair:
3.
Complete the following sentence to explain the meaning of #1 and #2: The cost to purchase ___________ gallons of propane is ___________ dollars.
Part B:
1.
Find g when C
(
g
)=
24.88
: g
=
¿
2.
Write your answer as an ordered pair: 3.
Complete the following sentence to explain the meaning of #1 and #2: If the cost to purchase propane was ______ dollars, then the number of gallons purchased was ________.
Part C.: Practical Domain: ¿
¿
≤ g≤
¿
gallons
Practical Range: ¿
¿
≤C
(
g
)
≤
¿
dollars
A local towing company charges $7.05 for each mile plus a $10 reservation fee. They tow a maximum of 20 miles. Let C(x) represent the total cost in dollars and x represent the number of miles driven.
Part A 1.
Calculate C
(
6
)
:
C
(
6
)=
¿
2.
Write your answer as an ordered pair:
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