Chapter Two

• More on Functions

• Review Definitions and Graphing of Functions with Calculator

Chapter 2

• More on Functions – Graphs of Functions

• Vertical Line Test• A set of points in a coordinate plane is

the graph of y as a function of x if and only if no vertical line intersects the graph at more than one point.

Relative Minimum

• Sometimes called local minimum

• Get graph of function

• Use CALC – minimum

• Could use trace and zoom.

Relative Maximum

• Sometimes called local maximum

• Get graph of function

• Use CALC – maximum

• Could use trace and zoom.

Walter Elliott

• “Perseverance is not a long race. It is many short races one after another.”

• Objectives• Graph a Step Function• Greatest Integer Function• Determine domain and range• Use the calculator

Objectives

• Graph Piecewise function

• Absolute Value function

• Determine domain and range

• Use the calculator

******Evaluate a Difference

Quotient

Objective

• Test for even and odd functions

• Even: f(-x) = f(x)

• Odd: f(-x) = -f(x)

Chinese Proverb

•“Better to light a candle than to curse the darkness.”

116 – Chapter 2 BittingerAlgebra of Functions

• Objective:

• Add, subtract, multiply, and divide functions.

( )( ) ( ) ( )

( )( ) ( ) ( )

( )( ) ( ) ( )

( )( )

( )

f g x f x g x

f g x f x g x

fg x f x g x

f f xx

g g x

Composition of two functions

( )f g x f g x

Objective

–Find compositions of one function with another function.

Hans Selye

• “Adopting the right attitude can convert a negative stress into a positive one.”

• 116- Transformations

• Shifting and Reflection and Stretching Graphs – Translation of Graphs

Objective: Recognize graphs of Common functions

• Constant

• Identity, Linear

• Absolute value

• Square root – cube root

• Quadratic function – Cubic Function

• Greatest Integer Function

Objective: Use vertical shifts

( ) ( )g x f x k

Objective: Use horizontal shifts

( ) ( )g x f x h

Objective: Reflection of Graph

( ) ( )g x f x

Albert Szent-Gyorgyi

• “Discovery consists of seeing what everybody has seen and thinking what nobody has thought.”

Objective: Absolute Value

( ) ( )g x f x

Objective: Put it all together

( ) ( )g x a f x h k

Albert Szent-Gyorgyi

• “Discovery consists of seeing what everybody has seen and thinking what nobody has thought.”

Hans Selye

• “Adopting the right attitude can convert a negative stress into a positive one.”

Def: Direct Variation

• The value of y varies directly with the value of x if there is a constant k such that y = kx.

Objective

• Solve Direct Variation Problems

• Determine constant of proportionality.

Procedure:Solving Variation Problems

• 1. Write the equation • Example y = kx• 2. Substitute the initial values and

find k.• 3. Substitute for k in the original

equation• 4. Solve for unknown using new

equation.

Example: Direct Variation

• y varies directly as x. If y = 18 when x = 5, find y when x = 8

• Answer: y = 28.8

Helen Keller – advocate for he blind

•“Alone we can do so little, together we can do so much.”