Math 102/Chapter 3

Chapter 3: Functions and Graphs

Chapter 3: Functions and their graphs

• Functions
• Graphs of functions (SKIP)
• Properties of functions
• Library of functions, piecewise functions
• Graphing transformations
• Building functions (modeling)

Section 3.1: Functions

Function relations

Maps and ordered pairs as relations

Determining whether a relation is a function

Determining whether an equation is a function

Finding values of a function

Finding values of a function on a calculator

Finding domain of function

Operations on functions

Section 3.2: Graph of function (SKIP)

Vertical line test

Identifying graphs that are or are not functions

Obtaining information from graph of function

Average cost function

Section 3.3: Properties of functions

Determining even and odd functions from graph

Determining even and odd functions algebraically

Determining where function is increasing, decreasing, or constant from grahp

Using graph to locate maxima and minima

Finding local maxima/minima from graph of function and determining where increasing/decreasing/constant

Finding absolute maxima and absolute minima for graph of function

Using graphing utility/calculator to locate local minima/maxima

Finding average rate of change

Finding equation of secant line (for rate of change applications)

Section 3.4: Piecewise functions

Graphing cube root function

Constant function, identity function, square function, cube function, cube root function, reciprocal function, absolute value function, greatest integer function, least integer function

Analyzing a piecewise-defined function

Application to cost of electricity

Section 3.5: Transformations

Vertical shift up

Vertical shift down

Horizontal shift right

Horizontal shift left

Combining vertical and horizontal shifts

Vertical stretch

Vertical compression

Graphing using stretches and compressions

Reflection about x-axis

Reflection about y-axis

Determining function obtained after series of transformations

Combining graphing procedures

Combining graphing procedures

Section 3.6: Mathematical models

Finding distance from origin to point on grpah

Area of rectangle

Making playpen

Chapter 3 Objectives

Section 3.1:

• Determine whether a relation represents a function
• Find the value of a function
• Find the domain of a function defined by an equation
• Form the sum, difference, product, and quotient of two functions

Section 3.2:

• IDentify the grpah of a function
• Obtain information from or about the graph of a fucntion

Section 3.3

• Determine even and odd functions from a graph
• Identify even and odd functions from the equation
• Use a graph to determine where a function is increasing or decrasing
• Use graph to locate local min max
• USE grpah to locate abs min miax
• Use graphing utility to locate approx local min max
• Find average rate of change of function

Section 3.4:

• Graph functions listed in library of functions
• Graph piecewise defined functions
• Graph functions using vertical and horizontal shifts
• Graph functions using compressions and stretches
• Graph functions using reflection about x-axis or y-axis
• Build and analyze functions