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I

Fall 2015

Term Test 1

Exam Guide

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Dependent

Variable

Independent

Variable

Calculus I Early Transcendentals ( 8 Edition )

by James Stewart

Chapter 1 Functions and Models

1.1 Four Ways to Represent a Function

1. What’s Function?

A function f is a rule that assigns to each elements x in a set D exactly one element, called f(x), in set E.

x f f(x)

Example:

A is a function of r, the number of A is called the value of A at r. If r = 2, the A = 4π. 4π is the value of A at

r = 2.

Important Note:

Composed Functions:

Given two functions f and g, the composed function f ◦ g is defined by: (f ◦ g) = f (g ()).

Past Exam Question:

1. f() = +1, g() = . Find f ◦ g and g ◦ f.

Solution:

f ◦ g() = f (g ()) g ◦ f(x) = g (f())

= f () = g ( +1)

= =

2. f() = +2, g() = , h() = 2. Find f ◦ g ◦ h.

Solution:

f ◦ g ◦ h () = f ( g ( h() ) )

= f ( g (2 ) )

= f ()

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= f ( 4) = ( 4) +2 = 4 + 2

2. Domain & Range

Domain: The domain of a function denoted by f is the set of points f is defined on.

Range: The range of a function denoted by f is the set of values that f(x) takes.

Example:

f() = , x R, f(x) .

Domain: (

Range: [ 0,

Important Note:

Let f(x) domain is D, g(x) domain is E, then, the domain of f ◦ g() = f (g ()) is │;

Similarly, the domain of g ◦ f(x) = g (f()) is .

Past Exam Question:

1. f(x) = 2x + 3, for all x g(x) = x – 1, , for all x . Find f ◦ g() and state its domain.

Solution:

f ◦ g() = f (g ()) = f ( x – 1) = 2(x – 1) + 3

= 2x + 1

The domain of f ◦ g() =

=

=

=

=

2. Find the domain of f(x) =

.

Solution:

The domain of f(x) =

=

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