MATHEMATICS 1000

Calculus I

Lesson #1

OBJECTIVES OF THIS LESSON

Distinguish notation for intervals and

functions.

Analyze inequalities, absolute value, and

absolute value inequalities.

Adopt basic analytic geometry concepts.

Adopt concepts of domain and range of a

function.

OBJECTIVES CONT’D

Perform the generalized graphing of common

functions such as:

Straight line

Quadratic

Square root

Absolute-value

NOTATION FOR INTERVALSThis lectures covers pages 1 – 11, sections 1.1 – 1.5.

a bo o

INEQUALITIES

1.

2.

3.

4.

ABSOLUTE VALUE

ABSOLUTE VALUE INEQUALITIES

if and only if

Example #1

which implies

SOME ANALYTIC GEOMETRY

A

B

ANALYTIC RESULT

DOMAIN AND RANGE OF A FUNCTION

http://www.youtube.com/watch?v=Ie_TExJdC

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Now for a short video:

GRAPHING “COMMON” FUNCTIONS

1. Recognize function type and recall general

shape.

2. Make note of Domain.

3. Create table of values.

4. Plot points and join appropriately.

Common Steps to Produce Graph

STRAIGHT LINE PLOT

General Form:

Example:

EXAMPLE #1 RESULT

Does your plot look like this?

What did you do wrong or right?

QUADRATIC FUNCTION PLOT

General Form:

Example:

EXAMPLE #2 RESULT

Does your plot look like this?

What did you do wrong or right?

SQUARE-ROOT FUNCTION PLOT

General Form:

Example:

EXAMPLE #3 RESULT

Does your plot look like this?

What did you do wrong or right?

ABSOLUTE VALUE FUNCTION PLOT

General Form:

Example:

EXAMPLE #4 RESULT

Does your plot look like this?

What did you do wrong or right?