 We saw yesterday that every relationship between x- and y-values represent a relation.  That means every graph on a coordinate grid represents a relation

 How can we write this relation down?  As ordered pairs, a table, or a mapping diagram.  {(1,5),(3,5),(4,2),(6,-2)}  Is it a function?

 How can we write this relation down?  We cannot write every point on this graph down – there is always another in between so the only way is to write an equation.  y = 2x + 4  Is this a function?

 D: {1,3,4,6}  R: {-2,2,5}

 D: x can be anything  R: y can be anything  A better way is to use set notation

To use the symbols of algebra, we could write the domain as Does that look like a foreign language? Let’s translate:

The curly braces just tell us we have a set of numbers.

The x reminds us that our set contains x-values.

The colon says, such that

The symbol that looks like an e (or a c sticking its tongue out) says, belongs to or is an element of...

And the cursive, or script, R is short for the set of real numbers.

R, the set So we read it, “The set of xsuch that x belongs to of real numbers.”

“The set of y, such that y belongs to R, the set of real numbers.” Read this:

the domain and range can be any real number. It is not always true that Sometimes mathematicians want to study a function over a limited domain.

 What do you think of the domain?  What about the range?

 What do you think of the domain?  What about the range?  Function or not?

 What do you think of the domain?  What about the range?  Function or not?

HW Worksheet Domain and Range

When we know that a relation is a function, the “y” in the equation can be replaced with f(x). f(x) is simply a notation to designate a function. It is pronounced ‘f’ of ‘x’. The ‘f’ names the function, the ‘x’ tells the variable that is being used.

Since the equation y = x - 2 represents a function, we can also write it as f(x) = x - 2. Find f(4): f(4) = f(4) = 2

If g(s) = 2s + 3, find g(-2). g(-2) = 2(-2) + 3 = = -1 g(-2) = -1

If h(x) = x 2 - x + 7, find h(2c). h(2c) = (2c) 2 – (2c) + 7 = 4c 2 - 2c + 7

If f(k) = k 2 - 3, find f(a - 1) f(a - 1)=(a - 1) (Remember FOIL?!) =(a-1)(a-1) - 3 = a 2 - a - a = a 2 - 2a - 2

 pg 635 #2, 4, 6, 8 (no sketch)

 Solve the equation for y.  Substitute any value for x and find how many answers it produces for y.  One: function  More than one: not a function  2x + 4y = 8  y = -0.5x + 2  This equation produces one output for every input so it is a function

This equation will produce two outputs for every input and is therefore not a function

 If and find:

 If and find:

 If and find:

 Worksheet

 Finding and Graphing