Pre Algebra (Period 1)

Relations & Functions 8-1

Look at p. 384-5 together - graphs of real world relationships
RELATIONS: Set of ordered pairs where
the x values are the DOMAIN and

the y values are the RANGE.

(You can remember which is which because it's alphabetic...
D comes before R just as x comes before y!)



FUNCTIONS: Relations where there is just one y value for each x value

IN OTHER WORDS----YOU CAN'T HAVE TWO y VALUES for the SAME x value!!!

If you see x repeated twice, it's still a relation, but it's not a function.

So, KEEP YOUR EYES ON THE x's!

AS LONG AS YOU DON'T SEE AN x REPEATED, YOU'VE GOT A FUNCTION!

In the real world, I have a good example...pizza prices.
You can't have two different prices for the same size cheese pizza.

If you charge $10 and $12 on the same day for the same pizza, you don't have a function.


But, you certainly can charge $10 for a cheese pizza and $12 for a pepperoni pizza.



VERTICAL LINE TEST: When you graph a function, if you draw a vertical line anywhere on the graph, that line will only intersect the function at one point!!!!


If it intersects at 2 or more, it's a relation, but not a function.

So a horizontal line function, y = 4, is a function, 
but a vertical line function, x = 4 is not.

INPUTS: x values (also the Domain)

OUTPUTS: y values (also the Range)

Graphing A Line 8-2
You can graph a line by making an x y table

Pick an x value

Plug in the equation to find the y

Graph the (x, y) for 3 points and connect



Slope of a Line 8-3
Slope is a formula. The slope is a constant along the entire line!

You can think of the slope of a line as the slope of a ski mountain -
When you're climbing up, it's positive

When you're sliding down, it's negative
(if you're looking at the mountain from left to right)


The steeper the mountain, the higher the slope

(A slope of 6 would be an expert slope because it

is much steeper than a slope of 2 which would be an intermediate's slope)

"Bunny slopes" for beginners will be lower numbers, generally fractional slopes (like 1/2 or 2/3)


A good benchmark to know is a slope of 1 or -1 is a 45 degree angle


You can also think of slope as rise/run - read this "rise over run"

Rise is how tall the mountain is (the y value)

Run is how wide the mountain is (the x value)

A 1000 foot high mountain (the rise) is very steep if it's only 200 feet wide (the run) (slope = 5)


Another mountain that is also 1000 feet high is not very steep if it is 2000 feet wide (slope = 1/2)



You can think of slope as a calculation:

Rise = Change in y value = Difference in y value = y₂ - y₁

Run=Change in x value Difference in x value x₂ - x₁



To calculate slope you need 2 coordinates. It doesn't matter which one you start with.

Just be consistent! If you start with the y value of one point, make sure you start with the same x!



Special slopes:
Horizontal lines in the form of y =
have slopes of zero (they're flat!)

Vertical lines in the form of x =
have no slope or undefined because the denominator is zero



Y INTERCEPT

Where the line crosses the y axis
y = mx +b
the m represents the slope and
the b represents the y intercept-- or where the line crosses the y axis!!

 CHAPTER 13-2: GRAPHING PARABOLAS

You will do this in Algebra

For the STAR you just need to know a couple of things to make an educated guess:

you will have a PARABOLA when the x term is SQUARED
A PARABOLA looks like
 a smile when the a coefficient is positive
or looks like a frown when the a coefficient is negative.
 
Example:
y = 3x² -2

The coefficient of the x² term is POSITIVE 3 so it's a smile.
The NEGATIVE 2 means the smile starts at -2
 Example:
y = -2x² +7 the coefficient of the x² term is NEGATIVE 2 so it's a frown.
The POSITIVE 7 means the frown starts at +7