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Section 2.2: Functions and Graphs 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: Graphs of Functions: We can use a table of values to make a graph. Be sure to consider the domain of the function when choosing values for the table. EXAMPLE: Graph the function and state its domain: f(x) = 2√x - 3 x f(x) Other Examples to Consider: 1) Find the value(s) of a in the domain of f for which f(a) equals the given number: f(x) = x2 + 2x 2; f(a) = 1 2) Find the zeros of f: f(x) = 8 6x