Question 967427
Function


equation in the form of y = f(x).
there is only one value of y for each and every value of x.


Relation


equation in the form of y = f(x).
there can be more than one value of y for any value of x.
all it takes is one value of x to have more than one value of y associated with it and the equation is a relation and not a function.



Vertical Line test


vertical line test is used to determine if you have a function or a relation.
if the vertical line only intersects with one value of y, then you have a function.
if the vertical line intersects with more than one value of y, then you have a relation.


Transformation


the graph of an equation is either moved or flipped over or stretched or shrunk by some formula.



Absolute Value Functions for f(x) = |x-2|


f(x) = |x-2|


if (x-2) is positive, then absolute value of (x-2) is equal to (x-2)
if (x-2) is negative, then absolute value of (x-2) is equal to -1 * (x-2).
in other words, the absolute value of an expression is always positive.\
you can get |x-2| = 0
you can get |x-2| = 5
you cannot get |x-2| = -5
|0| = 0
|5| = 5
|-5| = 5


Graphing Relations for x = 1 - y^2


equation is x = 1 - y^2
solve for y^2 to get y^2 = 1 - x
solve for y to get y = plus or minus square root of (1-x).
that graph will look like this.
{{{graph(400,400,-10,10,-10,10,sqrt(1-x),-sqrt(1-x))}}}
the vertical line test will tell you that this is a relation and not a function.


some references to help you:


<a href = "http://www.purplemath.com/modules/solveabs.htm" target = "_blank">http://www.purplemath.com/modules/solveabs.htm</a>


<a href = "http://www.purplemath.com/modules/fcns.htm" target = "_blank">http://www.purplemath.com/modules/fcns.htm</a>


<a href = "http://www.purplemath.com/modules/fcntrans.htm" target = "_blank">http://www.purplemath.com/modules/fcntrans.htm</a>


there's lots of references on the web.
just do a search and they'll pop up.
pick the ones that are easiest for you to understand.