Domain and Range by Semba04

Domain is associated with 'x' and
Range is associated with 'y'
always remember that!
________________________________

A relation is a set of ordered pairs (if you have a line or points on a graph you can have ordered pairs).

ex. (x, y), (3, 5), (4, -6), (-3, -1)

Domain is all the x values of a relation.

D = {x, 3, 4, -3}

Range is all the y values of a relation.

R: {y, 5, -6, -1}

Curly brackets are used to name the ordered pairs. I believe an = and : can be used interchangeably.


A function is when the x and y variables have something common and can be found using an equation.


Vertical Line Test
If a vertical line can be drawn to intersect more than exactly one point on a relation then that relation cannot be a function because it fails the vertical line test.

This states that if a line intersects its self on the (lets say) x axis it fails the vertical line test, so it is not a function.
________________________________








The relation of this diagram is:
(1, 5), (2, 6), (3, 5), (4, 6)
D: {1, 2, 3, 4}
R: {5, 6, 5, 6}
________________________________












This is a function
D: {'infinite'}
R: {'infinite'}
________________________________













This is not a function
D: {0, >5}
The domain is larger than zero
R: {0, >6}
The range is less than six
________________________________












This is a function
D: {<-5.5,>5.5}
R: {<0,>-5.5}
________________________________

This is not a function
D: {'infinite'}
R: {'infinite'}

________________________________

This is a function (notice how the circle on the bottom is not filled and the one on the top is. If the circle on the bottom was filled this would not be a function because those two points would overlap)
D: {<-6, >6}
R: {<-6, >6}
________________________________

Links for your knowledge (or entertainment): :)
Math Demos
Free Math Help
Bellingham High School Math
Purple Math

Everyting on this post was typed by me, by myself accept the vertical line test which I took from my notes from last year.