Math 102/Chapter 3
From charlesreid1
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