Sullivan Algebra & Trigonometry: Section 3.2 The Graph of a Function Objectives Identify the Graph of a Function Obtain Information from or about the Graph of a Function

When a function is defined by an equation in x and y, the graph of the function is the graph of the equation, that is, the set of all points (x,y) in the xy-plane that satisfies the equation. Vertical Line Test for Functions: A set of points in the xy-plane is the graph of a function if and only if a vertical line intersects the graph in at most one point.

x y Example: Does the following graph represent a function? The graph does not represent a function, since it does not pass the vertical line test.

Example: Does the following graph represent a function? The graph does represent a function, since it does pass the vertical line test. x y

The graph of f(x) is given below (0, -3) (2, 3) (4, 0) (10, 0) (1, 0) x y

What is the domain and range of f ? Domain: [0,10] Range: [-3,3] Find f(0), f(4), and f(12) f(0) = -3 f(4) = 0 f(12) does not exist since 12 isn’t in the domain of f

Does the graph represent a function? (0, -3) (2, 3) (4, 0) (10, -3) (1, 0) x y (7, -3) Yes

For which x is f(x)=0? (0, -3) (2, 3) (4, 0) (10, -3) (1, 0) x y (7, -3)