advertisement

2.3 Represent Relations and Functions 2.1-2.3 Quiz: FRIDAY Vocabulary: • A relation is a mapping, or pairing, of input values with output values. • The domain of a relation is the set of input values (x-values) • The range of a relation is the set of output values (y-values). • A function is a relation for which each input value has exactly one output value. x-values CANNOT repeat! Vocabulary • Vertical Line Test By the vertical line test a relation is a function if and only if no vertical line intersects the graph of the relation at more than one point. More Vocabulary • An equation in two variables has an independent variable, and a dependent variable, that depends on the value of the independent variable. • An ordered pair (x, y) is a solution of an equation in two variables if substituting x and y into the equation produces a true statement. • The graph of an equation in two variables is the set of all points (x, y) that represent solutions of the equation. Yes….More Vocabulary • A linear function can be written in the form y = mx + b where m and b are constants, or in function notation f(x) = mx + b. • A function is one-to-one if no two values in the domain have the same value in the range. y-values CANNOT repeat for the function to be one-to-one. Example 1: • Consider the relation given by the ordered pairs (1, 0), (0, -2), (-2, 3), (3, 1) Identify the domain and range Represent the relation using a graph Use the vertical line test to tell whether the relation is a function If the relation is a function, tell whether it is a one-to-one function. Example 1 Cont’d: • D: -2, 0, 1, 3 R: -2, 0, 1, 3 • The relation IS a function. • The relation IS one-to-one Example 2: • Graph the equation y = -2x – 2 Example 3: • Tell whether the function is linear. Then evaluate the function when x = -3 a) f(x) = 6x + 10 b) g(x) = 2x2 + 4x – 1