MATH 207 Introduction Review

MATH 207 Introduction Review

WHY CALCULUS?

Brightspace: brightspace.ccc.edu What is it? It replaces Blackboard. Adios Blackboard! How do I log in? With my ccc credentials (login and password) DO it now! (on your tablet/phone…) Set up your profile to get my messages. Look around the contents.

Syllabus Let’s go over it in detail. Please pay attention. I will be giving you a short quiz next time about its contents!

A couple more things…

Lunch (!) I realize our class meets during a common time for lunch, however, please refrain from bringing a full meal to class! If you must eat, please choose a discreet -(ie: no smells and noises)- snack only.

About you At the end of today’s session: turn in the “Who Am I” handout I gave you. Fill in as much as is comfortable for you on it. All info will be appreciated and will help to get to know you better. Let’s go around and mention our Name and Superpower 

Now let’s review a few things…

Several review links are posted on the class website! For example: PreCalculus Tutorials MATH2.org  Midnight Tutor Videos Just Math Tutorials NeededForCalc.pdf

Distance Formula Answer: 6.71 Example: Find distance between (-1,4) and (-4,-2). Answer: 6.71

Midpoint Formula Answer: (-4,3) Example: Find the midpoint from P1(-5,5) to P2(-3,1). Answer: (-4,3)

Example: Circle Equations Equations in two variables – Example: Circle Equations x y (h, k) r (x, y) The standard form of an equation of a circle with radius r and center (h, k) is: The Unit Circle equation is:

Copyright © Cengage Learning. All rights reserved. Four Ways to Represent Functions 1.1 Copyright © Cengage Learning. All rights reserved.

Definition of a Function

It’s helpful to think of a function as a machine: The input is the independent variable, The output is the dependent variable.

Four Ways to Represent a Function verbally (by a description in words) numerically (by a table of values) visually (by a graph) algebraically (by an explicit formula)

Verbally (with words) or With Diagrams: Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Numerically: using Tables -

Visually: using Graphs -

Algebraically: using Formulas – There are several Categories of Functions:

The most common method for visualizing a function is its graph The most common method for visualizing a function is its graph. If f is a function with domain D, then its graph is the set of ordered pairs: {(x, f (x)) | x  D}

Theorem: Vertical Line Test A set of points in the xy - plane is the graph of a function if and only if a vertical line intersects the graph in at most one point.

Piecewise-defined Functions: Example: Example:

A common Piecewise Defined Function: Absolute value function: f (x) = |x| x if x  0 f(x) = |x| = –x if x < 0

Symmetry

Odd and Even Functions If a function f satisfies f (–x) = f (x) for every number x in its domain, then f is called an even function. The graph of an even function is symmetric with respect to the y-axis If f satisfies f (–x) = –f (x) for every number x in its domain, then f is called an odd function. The graph of an odd function is symmetric about the origin An even function Figure 19

Increasing and Decreasing Functions

Where is the function increasing?

Where is the function decreasing?

Where is the function constant?

Average rate of change of a Function

From 0 to 1

Local Maxima and Minima

Local Min

Average rate of change of a Function

From 0 to 1