Section 4.1: Relations and Functions
Relation : Any set of ordered pairs
Domain: The set of all first coordinates (x­values)
Range: The set of all second coordinates (y­values)
Relations can be described
• with a set of ordered pairs
• with an equation in two variables
• with a graph on the Cartesian Plane
Function: • A relation in which every element of the domain is paired with exactly one element of the range. • For every "x" there is only one, unique "y".
• A relation in which no two distinct ordered pairs have the same first coordinate.
Examples:
Vertical Line Test for Functions: If you can draw a vertical line that intersects the graph of a relation in more than one point, the graph does NOT represent a function.
Examples:
Function Notation: • gives a name to the function
• provides a formula
• describes the relationship of the dependent variable (usually "y") in terms of the independent variable (usually "x").
• f(x) is read "function of x" or "f of x". • f(x) does not represent the product of f and x.
Evaluating Functions: replace the independent variable with a particular "value" and simplify.
Examples:
Implied Domain of a Function: Usually the domain of a function is assumed to be all real numbers. However, sometimes we must limit the domain to be sure no values will cause the function to be undefined.
We must:
• exclude any values that will cause division by zero (undefined)
• exclude any values that will cause the even root of a negative number (not real)
Examples: