1. Properties of Functions Operations on Functions
Lessons 2.1, 2.3, 2.4, and 2.6
Functions
Properties of Functions
Library of Functions
Operations on Functions

2. Relations and Functions
Any correspondence
between two sets
(x,y)
Functions:
Is a relations that associates with each element of x exactly one element of y.
Vertical Line Test

3. Key Words Related to Functions
Domain and Range
Value: given x what is the value of y?
One-to-one correspondence
Independent and Dependent Variable
Explicit and Implicit Form
Even or Odd Functions

4. Obtaining Information from the Graph of a Function
Domain and Range
x and y-intercepts
Symmetry – Even or Odd
Increasing, decreasing or constant
Local Maxima, Local Minima

5. Function Notation y = f(x) f is a symbol for the function
x is the independent variable
y is the dependent variable
f(x) is the value of the function (y) at x

6. Library of Functions Linear function Constant function
Identity function
Square function
Cube function
Square Root function
Reciprocal function
Absolute Value Function
Greatest-Integer Function (A only)

7. Piecewise Functions functions defined by more than one equation
Ex. The absolute value function is an
example of a piecewise function.

8. Operations on Functions
Functions like numbers can be added, subtracted, multiplied, and divided.
f + g, f – g, fg, f/g
The domain of f +g, f – g, and fg consists of all numbers x in the domain of both f and g. (intersection of two domains)
The domain of f/g consists of all numbers x in the domain of both f and g for which g(x) is not equal to zero.

9. Composition of Functions
Notation: f (g (x)) or f o g, where f is the outer function and g is the inner function.
The domain of a composition is the set of all numbers x in the domain of the inner function that satisfy the composition.
Decomposition: the process by which you find the components of a composite function.