2.1+Representing+Relations+and+Functions

=**__ Functions and Relations __**=

Ex. (3,4) (5,3) (10,0)
These can be represented as a diagram or graph.

**__ Domain and Range __**
The domain = x-coordinates The range = y-coordinates.

So in the ordered pair ** (-2, -3), -2 ** is the ** domain ** and ** -3 ** is the ** range. **

In real life you may need to restrict the domain so it is reasonable in the given situation.

Lines connect the inputs with their outputs
[|Here] is a great place that explains functions. [|Click here]for a place that explains functions as well, but has an interactive problem solver to help you with problems.

**__ Table Functions __**
The easiest way to tell if a set of ordered pairs in a table is a function is to simply look at the x-coordinates.

In a table we have the set of ** (-2, -4), (-1, -4), (0, -4), (1, -4), and (3,-4). ** Is this a function? ** It is **. All the inputs (x- coordinates) have one output. Even though the output was the same, the inputs never had more than one output.

However if we had
 * (-2, 1), (-2, 5), (-1, 3), and (1, -2) **, this would not be a proper function. The input -2 has **more than one** output ( 1 and 5 ).

**__ Graphing Functions __**
Graphing functions is very easy. A graph can be a function if the points do not intersect the graph at more than one point. To check to see if it is a function, do the vertical line test. If the points form a vertical line, the graph is a proper function.



**__ Equations in two variables __**
Many equations can be described by an 'equation in two variables'. Such as y = 3x - 5.

x = the independent variable y = the dependent variable

//The dependent variable depends on the variable of the input value//.
An ordered pair (x, y) is a solution of an equation in in two variables if substituting x and y in the equation produces a true statement.

For example, **(2, 1) is a solution of y = 3x - 5** because when you substitute the numbers in then solve, the statement becomes true.

Ex: (x,y) (2,1) y = 3x - 5 1 = 3( **2** ) - 5 1 = 6 - 5  1 = 1
 * This statement is true. **

**__ Graphing an Equation __**
The graph of an equation in two variables is the set of all points (x,y), that represent solutiojns of the equations

There are three steps to follow while graphing an equation.
 * 1) Construct a table of variables
 * 2) Plot enough points from the table to recognize a pattern
 * 3) Connect the points with a line or curve.

**__ Linear Functions __**
What to know: y = mx+b - Linear Function (m and b are constants). f(x) = mx+b - Linear function in function notation. The linear function in function notation is read simply "f of x", x being the independent variable. If you want to graph a linear function, the way to tell if it is a linear function is to see if the points for a vertical line.

[|Click here]for an easy step by step video on solving f of x functions.