2.1 Functions
It’s a beautiful day, don’t let it get away.
-U2
Functions - Vocabulary
X-Variable
Y-Variable
• Domain of the function
• Range of the function
• Independent variable
• Dependent variable
• Control variable
• Set of Inputs
• Set of Outputs
“x corresponds to y”
“y depends on x”
Functions
A function is a relation in which each value of the control variable
x is paired with only one value of the dependent variable y.
Domain
FUNCTION
Range
Functions
A function is a relation in which each value of the control variable
x is paired with only one value of the dependent variable y.
Domain
FUNCTION
Range
Functions
A function is a relation in which each value of the control variable
x is paired with only one value of the dependent variable y.
Domain
NOT A
FUNCTION
Range
Function or Not?
Determine which of the following relations represents a function.
1) {(2,3),(1,0),(2,4),(10,1)}
2) {(3,1),(2,1),(4,5),(0,2)}
3) {(1,1),(2,2),(3,3),(4,4)}
Function or Not?
Determine which of the following relations represents a function.
2x  5
1) y 
x3
2) x  y 2
3) y   4 x
4) (x  2) 2  (y  4) 2  16
Function Notation
x 2 1
Find the following values for the function given: f (x) 
x4
1) f (2)
2)  f (3x)

x 2 1
f (x) 
x4
3) f (x 1)

Difference Quotient
The Difference Quotient:
f (x  h)  f (x)
h
Simplify the difference quotient given the following function.
f (x)  x 2  3x 1


Domain of a Function
The domain of a function is the set of all values of x for which
the f (x) is a real number.
Find the domain of the following function:
1) Polynomial function: f (x)  x 2  3x 1

Domain of a Function
The domain of a function is the set of all values of x for which
the f (x) is a real number.
Find the domain of the following function:
2x
2) Rational function: f (x) 
3x  5x 2

Domain of a Function
The domain of a function is the set of all values of x for which
the f (x) is a real number.
Find the domain of the following function:
3) Square root function: f (x)  5x  8

Computations of a Function
Given f and g below, find the following and determine the
g(x)  x 2  4
domain in each case. f (x)  x  3
1) ( f  g)(x)
2) (g  f )(x)

3) (g f )(x)
 f 
4)  ( x)
g 

Group Practice!!
2.1 Functions
Homework#16: p.69
#39, 47 – 59 Odd, 67,
69, 73 – 77 Odd
It’s a beautiful day, don’t let it get away.
-U2