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H-Intro to Calc Study Guide for Lessons 1.1 and 1.2
Section 1.1: Modeling and Equation Solving
1. Analyze the following table about the average annual cost to care for a pet ocelot, and
then answer the questions that follow:
able 1.7 U.S. Air Travel
Year
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
Average Annual Cost
$452.30
$475.10
$488.50
$528.80
$547.80
$581.20
$594.70
$612.90
$636.00
$666.10
a) Graph a scatter plot of the data (optional). Let x be the number of years since 1991.
(b) From 1991 to 2000 the data seem to follow a linear model. Use the 1991 and 2000 points
to find an equation of the line.
(c) According to the linear model, in what year did the average annual cost to care for a pet
ocelot seem destined to reach $900?
Functions: a relationship is a function if each input has exactly one output value.
Section 1.2: Determining if a Relationship is a Function
2. Determine whether the relationship is a function, and explain.
{(2,10),(3,15),(4,20),(3,25)}
{(3,1),(4,2),(5,1)}
Function?
Function?
Explanation?
Explanation?
Worksheet 1.2: Determining if a Graph is a Function
Determine which of the curves are graphs of functions.
function?
function?
function?
function?
function?
function?
function?
function?
Domain and Range
domain = set of values of x that are possible to plug into the equation
range = set of values of y that result when you plug in x
Determining the Domain
The domain is either all the real numbers (domain = (-∞,∞)), or is restricted – either by
context or by the impossibility of plugging in some values.
There are exactly two reasons why it would be impossible to plug in a value of x:
 you can’t take the square root of a negative number
 you can’t divide by 0
Section 1.2: Determining the Domain of a Function from Its Equation
Find the domain of the function, and describe the domain using interval notation.
8
1. f x   7 x  4
3. f  x   x  4
2. f  x  
x
4.
f x  
2
1  2x
5.
f x   6 x
6.
f x  
x4
Section 1.2: Determining the Domain and Range from a Graph
Describe the domain and range of each graph using interval notation.
(a) domain:
(a) domain:
(a) domain:
(a) domain:
(b) range:
(b) range:
(a) range:
(b) range: