Unit 3 - Objective 4 - Graph a Function

The graph of a function in two variables x and y is formed by all the points P(x,y) whose coordinates (x,y) satisfy the given functional relationship y = f(x).  We assume a certain value for x and then find the value of the function of x.  A graph can provide us with an easy test to see if a graph is a graph of a function. If no vertical line intersects the graph more than once then it represents a function.

Basic procedures

• Let x take on several values and calculate the cooresponding values of y.
• Plot the points.

Examples:

1. y = x2 - 3
 x y -3 (- 3)2 - 3 = 6 -2 (- 2)2 -3 = 1 -1 (- 1)2 - 3 = - 2 0 (0)2 - 3 = - 3 1 (1)2 - 3 = -2 2 (2)2 - 3 = 1 3 (3)2 - 3 = 6

(This graph is a function)

2.

 x y 0 1 4 9

(Notice that x cannot be a negative number and this graph is a function)

3. y = 1/x

 x y -3 1/(-3) = -1/3 -2 1/(-2) = -1/2 -1 1/(-1) = -1 -1/2 1/-(1/2) = -2 1/2 1/(1/2) = 2 1 1/1 = 1 2 1/2

(Notice that x cannot be equal to 0 because you
cannot divide by 0 and this graph is a function)