12
1. 2 Properties of Functions and Their Graphs
1. 2
Properties of Functions and Their Graphs
Some Basic Properties
Many properties of a function can be obtained from its graph.
Example 1: Domain, Range, Intercepts and Sign of the Function
The graph of f
1. 1 Functions
10
Exercises 1. 1
1. Determine which of the following graphs represent a function.
(a)
(b)
(c)
(d)
Evaluate the following functions at the indicated values. Simplify where possible.
2x
2+x
g (1), g (3), g (3/2), g (2a + 1), g (2 a)
2. f (x)
1. 1 Functions
1. 1
2
Functions
Introduction to Functions
Denition: A function f is a rule that assigns to each element x in one
set one and only one element y in another set. The element
y is often denoted by f (x), read "f of x" or "the value of
f at x"
Math 1022 General Syllabus - Fall 2012
Algebra Review
Beginning of Semester Review
Use any algebra book for reference. You can also visit math.temple.edu/nhamid/ClassNotes.html.
Check the MSRC Blackboard Organization for Math 1022 for any scheduled review
1. 2 Properties of Functions and Their Graphs
7
Exercises 1. 2
In Exercises 1 - 3, the graph of a function f is given. Determine
(a)
(b)
(c)
(d)
(e) the intervals on which f (x) > 0, if any
(f) the intervals on which f (x) < 0, if any
(g) if f is even, od
1. 3 Basic Graphs and Their Transformations
27
Exercises 1. 3
1. The graph of f is given. Sketch the following transformations of the graph of f .
4
3
2
f
1
4
3
2
1
1
2
1
3
4
(a) y = f (x) + 1
(b) y = f (x + 1)
(c) y = f (x)
(d) y = f (x 2) 1
(e) y = |f (
1. 5 Composition of Functions
37
Exercises 1. 5
For each pair of functions f and g , nd f g , g f , and their domains.
1. f (x) = 6x 1, g (x) = 2x + 5
4
x
3. f (x) = , g (x) =
2. f (x) = 5x2 2x + 1, g (x) = x 2
1
x5
2x
5
, g (x) =
x+3
x
6. f (x) = x2 + 1,