Function, Domain, Range, Rita Korsunsky

Relations and Functions A relation is a connection between 2 sets of numbers. For example, (x, y) The x-values represent the domain, and the y-values represent the range. x is the independent variable and y is the dependent variable.

Functions Function- A correspondence that assigns to every element in set D EXACTLY one element in set R. Set D = domain; Set R = range. A function Not a function D R 5 6 8 10 14 23 D R 5 6 8 10 14 23

Vertical Line Test Not a function Function

Representing Relations and Functions When a relation is also a function (passes a vertical line test), we often use “special” notation. For example, The mapping would be:

Practice Problems (in class) State the domain and range: {(3, 4) (1, 6) (2, 6)} Determine whether this mapping represents a function. Is this a function?

Example 1 Find a rule for the pairings given below. Write your rule in function notation. If I multiply the x-coordinate by 3, I get the y-coordinate. My rule is: domain range

Example 2 Is it a function? Yes, it passes the vertical line test. Find the domain and the range of this function

Example 3 Tell whether each graph is the graph of a function. If it is, give the domain and range of the function. 1 5 8 -2 Passes the vertical line test. Yes, function.

Example 4 Tell whether each graph is the graph of a function. Give the domain and range. Passes the vertical line test. No, not function.

Example 5 Tell whether each graph is the graph of a function. If it is, give the domain and range of the function. Passes the vertical line test. Yes, function.

Example 6

Special Functions You should know what the graphs of each of these 5 special functions look like.

Special Functions

Greatest integer Function For all real numbers, x, the greatest integer function returns the largest integer.

Practice Problems 4. For g(x)=2x-1 find g(3) and g(-2). Graph g(x). 5. If h(x)=2x over the domain {-3,1,4}, what is the range? Does –h(x)=h(-x)? Range = {-6,2,8}, yes