Math Comics

Link to MATH COMICS

 that I have collected over the years...

What is a FUNCTION?

A FUNCTION is...

a "RULE" that explains what mathematical operations will be APPLIED to:

- an INPUT (an "X") to produce the OUTPUT (the "Y" value)

- "X" (the INDEPENDENT VARIABLE)

- a NUMBER from the DOMAIN

-  to get the VALUE for Y (the DEPENDENT VARIABLE) from a given "X" VALUE

the DOMAIN is the set of possible "X" values

the RANGE is the set of  "Y" values

use letters like "f" or "g" or "h" ... to represent a function

f can also be thought of as a MAPPING (Arrow diagram) 

showing how (CONNECTS) each

value from the DOMAIN is

matched to a PARTNER in the RANGE

f can also be pictured as a MACHINE that takes

a given INPUT and produce a SINGLE OUTPUT

using a UNIQUE RULE

"x" is an INPUT and

"y" or "f(x)" is the OUTPUT value

f(x) is read as

- f of x

- f operating on x

- f evaluated at x

- the value of f at x

- the image of x under f

An employee for ACME INDUSTRY earns $9 for each hour worked.

To calculate the EARNINGS for a certain individual we

"Multiply the NUMBER OF HOURS (x) by 9"

g(x) = 9 times x

g(x) = 9x

suppose the DOMAIN is {20,30,40}

then the RANGE will be {180, 270, 360}

g(20) = 9(20) = 180

etc.

If ACME INDUSTRY changes the pay rate to $360 for any

employee that works less than or equal to 40 hours in a given week.

When an employee works more than 40 hours they receive an

additional $10 for each hour over 40. This creates the need for a

special type of function called a PIECEWISE DEFINED FUNCTION.

Two different rules are needed. One rule for less than or equal to 40 hours

and a second rule for over 40 hours.

g(x) = 360  .....................  if   0< x <= 40

g(x) = 360 + 10(x-40)  .... if 40 < x

REPRESENTING A FUNCTION:

1) VERBALLY (using words)

2) ALGEBRAICALLY (using a formula ... f(x) = 9x   )

3) VISUALLY (use a GRAPH)

4) NUMERICALLY (by use of TABLE)

Finding Square Roots 50 years ago

FINDING SQUARE ROOTS
WITHOUT TECHNOLOGY

solving equations

Here are examples with Fractions in the Equations.

Look at #4 for logical steps to follow.

Usually by clicking on an image
you can see a LARGER VIEW.

 

***********************

Below are more simple

type equations

Humorous quotes about Mathematics

Animated Whiteboard Presentations

SOMETHING NEW FOR ME (Animated Whiteboard presentations):

FACTORING VIDEOS (New as of Feb., 2015)

VIDEO - on Problem 45
VIDEO - on Roots and Absolute Values
VIDEO - Adding Radicals
VIDEO - Two Ways to do a Fraction with Radicals
VIDEO - on using Conjugates
VIDEO - on when to simplify a radical
VIDEO - Combinations & Factorials 
VIDEO - Functions

matrices and determinants

 As of Feb. 9th (CLICK HERE!) we will be using a site that I have been building. It is an explanation of MONOMIALS and POLYNOMIALS

Below is Problem 39 using the ti-83

THE TI-83 to solve 3 equations and 3 unknowns

AUGMENT MATRIX SOLUTIONS

AUGMENT MATRIX SOLUTIONS

 How about another example?  

  How about another example?

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In problems 7 thru 12 you probably need to
MULTIPLY the FRACTIONS into
the RED MATRIX to get the FINAL INVERSE MATRIX

I HOPE THE PROBLEMS ABOVE ARE THE ONES YOU ARE WORKING ON!