ALGEBRA 2 LECTURE F – 2: Functions
Reading Assignment: Chapter 2, Pages 102 – 132
FUNCTION DEFINITION

A function is a relationship between two variables such that each value of the first
variable is paired with exactly one value of the second variable.


The domain of a function is the set of all possible values of the first variable (x).
The range of a function is the set of all possible values of the second variable (y).

You can use the vertical-line test to determine if a graph represents a function.
ALGEBRA 2 LECTURE F – 2: Functions
DISCRETE and CONTINUOUS FUNCTIONS


A function that is defined only for a set of numbers that can be listed, such as the set of
whole numbers or the set of integers, is called a discrete function.
A function is continuous when its graph is a single unbroken curve.
FUNCTION NOTATION
ALGEBRA 2 LECTURE F – 2: Functions
TRY THIS Page 104: Let the first variable, R, represent checking and savings account
customers at a local bank. Let the second variable, N, represent checking and savings account
numbers. Is the relationship between R and N a function? Explain.
TRY THIS Page 105: State the domain and range of each function graphed.
A. Domain:
Range:
B. Domain:
Range:
OPERATIONS WITH FUNCTIONS

For all functions f and g:
 Page 114 #4 – 7: Let f(x) = x/2 and g(x) = 3x + 1.
4. f + g =
5. f – g =
6. f  g =
7. f / g =
ALGEBRA 2 LECTURE F – 2: Functions
 TRY THIS Page 112: Let f(x) = – 7x2 + 12x + 2.5 and g(x) = 7x2 – 5
Find f + g
Find f – g
 TRY THIS Page 112: Let f(x) = 3x2 + 1 and g(x) = 5x – 2
Find f  g
Find f / g
COMPOSITION OF FUNCTIONS
 Let f a g be functions of x
 The composition of f with g, denoted f ∘ g, is defined by f (g(x)).
 The function f ∘ g is called the composite function of f with g.
 Page 114 #8 – 9: Let f(x) = x/2 and g(x) = 3x + 1.
8. f ∘ g =
9. g ∘ f =
TRY THIS Page 113: Let f(x) = – 2x2 + 3 and g(x) = – 2x
Find f ∘ g
Find g ∘ f
ALGEBRA 2 LECTURE F – 2: Functions
INVERSES OF FUNCTIONS
 The inverse of a relation consisting of the ordered pairs (x,y) is the set of all
ordered pairs (y,x).
 The domain of the inverse is the range of the original relation.
 The range of the inverse is the domain of the original relation.
 Page 122 #8 Find an equation for the inverse of y = 3x +9
TRY THIS Page 119: Find an equation for the inverse of y = 4x – 5
HORIZONTAL-LINE TEST
 The inverse of a function is a function if the original function was a one-toone function.
 The inverse of a function is a function if and only if every horizontal line
intersects the graph of the given function at no more than one point.
COMPOSITION AND INVERSES
 If f and g are functions and (f ∘ g)(x) = (g ∘ f)(x), then f and g are inverses of
one another.
 Page 122 #10: Verify that F(x) = 6x – 5 and g(x) = 1/6 x + 5/6 are inverses
of each other.
TRY THIS Page 121: Show that f(x) = –5x + 7 and g(x) = –1/5x + 7/5 are inverses
of each other.
HW F – 2:
Pages 108 – 109 #17, 21, 25, 27, 29, 31, 33, 39, 41, 43, 45, 67, 69
Pages 115 – 116 #13, 15, 17, 21, 35, 39, 43, 45, 63
Pages 122 – 123 #13, 17, 19, 25, 27, 29, 33, 51