The Graph of a function Objectives: Identify the graph of a function Obtain information from or about the graph of a function

Graph of the Function In applications, a graph often demonstrates more clearly the relationship between two variables then say an equation or table would. The graph of the function is the set of points in the xy-plane that satisfies the equation. Not every collection of points in the xy-plane represents the graph of a function. The graph must satisfy the Vertical Line Test: a set of points in the xy-plane is the graph of a function if and only if every vertical line intersects the graph in at most one point.

EX 1: Use the graph of the function f given below to answer parts a - k a) Find b) Is positive or negative ? c) For what numbers x is ? d) What is the domain of ? e) What is the range of ? f) Is a function?

EX: Use the graph of the function f given below to answer parts a - k g) What are the x-intercepts? h) What is the y-intercept? i) How often does the line intersect the graph? j) For what value of x does k) What type of symmetry?

EX 2: Answer the questions about the given function a) Is the point on the graph of ? b) If , what is ? What point is on the graph of ? c) If , what is ? What point(s) are on the graph of ?

EX 2: Answer the questions about the given function d) What is the domain of ? e) List the x-intercepts, if any, of the graph of f) List the y-intercepts, if any, of the graph of