Function Domain Range Rita Korsunsky Relations and Functions

Relations and Functions A relation is a connection between 2 sets of numbers. For

Functions Function A correspondence that assigns to every element in set D EXACTLY one

Vertical Line Test Function Not a function

Representing Relations and Functions When a relation is also a function (passes a vertical

Practice Problems (in class) 1. State the domain and range: {(3, 4) (1, 6)

Example 1 Find a rule for the pairings given below. Write your rule in

Example 2 Is it a function? Yes, it passes the vertical line test. Find

Example 3 Tell whether each graph is the graph of a function. If it

Example 4 Tell whether each graph is the graph of a function. Give the

Example 5 Tell whether each graph is the graph of a function. If it

Special Functions You should know what the graphs of each of these 5 special

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

Practice Problems 4. For g(x)=2 x-1 find g(3) and g(-2). Graph g(x). g(3) =

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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 D R Not a function D R 5 10 6 14 8 23

Vertical Line Test Function Not a 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) 1. State the domain and range: {(3, 4) (1, 6) (2, 6)} Domain: {1, 2, 3} Range: {4, 6} 2. Determine whether this mapping represents a function. no, yes, no 3. Is this a function? 3 and 3 are the same value no

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 ycoordinate. 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. 8 Passes the vertical line test. Yes, function. 1 1 -2 -2 5

Example 4 Tell whether each graph is the graph of a function. Give the domain and range. Does not pass 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)=2 x-1 find g(3) and g(-2). Graph g(x). g(3) = 5 and g(-2) = -5 5. If h(x)=2 x over the domain {-3, 1, 4}, what is the range? Does –h(x)=h(-x)? Range = {-6, 2, 8}, yes