Linear Function

015B

So, I definitely want to talk about Linear Functions.  You may have reached this page because you had trouble answering question 015A of the AMAZEing Math Maze.  Or you just wanted to know about Linear Functions.  Let's start with the Maze. 

Question 015A was about Bob and his figurines.  Every month we added 3 figurines to the total number of Bob figurines.  If you look at this, you should notice that the number of figurines increases by 3 each month.  That is a steady linear rise.  The correct answer was Linear.  Let's talk about Linear Functions a bit and then ask question 015B.

Linear Functions explained

The key part of of the word Linear is the first 4 letters LINE!  These functions form a straight line when plotted on a piece of graph paper.  the equation will be in the form y = ax + b where a and b are constant numbers.

Quadratic functions are of the form

y = ax2 + bx + c

when graphed it will form a parabola which looks like this -

Exponentials are of the form

y = 3x

And they look similar to this.  Growth or decay starts at a point and then rises (or falls) in ever increasing jumps.

And, while we're at it, let's talk a little about Absolute Values.  This is when the portion of the equation within the brackets is positive such as y = | 2x | + 7.  The 2x is positive regardless of what value we let x be.  So, the graph of an absolute value is mirrored about a line representing where the value of the stuff inside the straight line brackets turns to negative and then back to positive by the brackets.  Anyway, for a linear function it looks like this -

Question 015B!!

Bob is getting better and better at laying bricks.  He gets paid by the brick, and each week he makes 2 more dollars than the previous week.  It's starting to look like he will keep improving at this rate forever!  One could say his skill level increases at a ____________  rate.

a) Linear

b) Quadratic

c) Exponential

d)  Diminished

For a more complete explanation of Linear Function you may want to check with Columbia University in New York.  When I tried to look up the "official" definition, the dictionary type sites referred me to linear transformations.  Not very satisfying as linear transformations isn't really what we're looking for here.  Any way Columbia University does a pretty good job of explaining things in detail with examples. 

I confess, when I try to explain things I pretty much just wing it (Perhaps you've noticed).  Again, if you're looking at this stuff and thinking - dang, I could do better than this!  I believe you!  Please, let me know as I could definitely use some help.  I get 2 or 3 calls a week from people who would love to help and they explain in great detail that it would be well worth the $500 to make my site look more professional.

My goal is to look less professional and more informative.  There are a lot of really good math sites who have enough money to look super professional.  Any suggestions are appreciated.  And if you're not in a totally altruistic mood (I understand), I will even discuss a way I've come up with to pay you from the vast profits of this site.  (As of this writing, there have been no profits)

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