Bell Ringer Write on a Post-it your answer to the following question. Write anything you know about functions (on the post-it you received)? Notation How to manipulate. Simplify Inverse

Chapter 1: Functions and Models 1.1 Four Ways to Represent a Function

Function: Usually denoted “f ”, it assigns each element x (from the domain) to exactly one element called f(x) or sometimes y (in the range). The elements of the domain, x’s, are called independent variables. The elements of the range, y’s, are called dependent variables.

Functions can be presented as graphs: Find f(1) f(1)=3 Find f(5) f(5) -0.7

There are four ways to represent a function: Verbal: a description in words Numerically: a table of values Visually: a graph Algebraically: a formula or equation

Vertical Line Test A curve (graph) in the x-y plane is a function if and only if no vertical line intersects the curve more than once.

Piecewise Defined Functions These are functions that are defined by different formulas in different parts of their domains. Here is an example of a piecewise function: Piecewise functions are also called “compound functions”.

The Absolute Value Function Value is ALWAYS positive. Given as a piecewise function: Some clarifying examples:

Symmetry Even function: f(-x)=f(x) for every x in its domain. For example: Odd function: f(-x)=-f(x) for every x in its domain. For example:

Increasing/Decreasing A function is called INCREASING if on an interval I, A function is called DECREASING if on an interval I,   f ( x 1 ) > 2 whenever in I

Some examples before the assignment: Evaluate the difference quotient for The difference quotient is given by: Find the domain of: Sketch this compound function:

Decide whether each function is even, odd, or neither.

Assignment: Hughes-Hallett (HH) pp 7-9: 2, 4, 6, 8, 10, 16, 24, 28, & 34