Download presentation
Presentation is loading. Please wait.
Published byVivian Hall Modified over 6 years ago
1
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
2
Chapter 1: Functions and Models
1.1 Four Ways to Represent a Function
3
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.
4
Functions can be presented as graphs:
Find f(1) f(1)=3 Find f(5) f(5)
5
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
6
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.
7
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”.
8
The Absolute Value Function
Value is ALWAYS positive. Given as a piecewise function: Some clarifying examples:
9
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:
10
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
11
Some examples before the assignment:
Evaluate the difference quotient for The difference quotient is given by: Find the domain of: Sketch this compound function:
12
Decide whether each function is even, odd, or neither.
13
Assignment: Hughes-Hallett (HH)
pp 7-9: 2, 4, 6, 8, 10, 16, 24, 28, & 34
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.