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 Bittinger Algebra of Functions Objective: Add, subtract, multiply, and divide functions.

Composition of two functions

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

Objective: Use horizontal shifts

Objective: Reflection of Graph

Albert Szent-Gyorgyi “Discovery consists of seeing what everybody has seen and thinking what nobody has thought.”

Objective: Absolute Value

Objective: Put it all together

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.”