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

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

u3obj4-1.gif (3526 bytes)
(This graph is a function)


2. u3obj400.gif (157 bytes)

x y

0

u3obj42a.gif (522 bytes)

1

u3obj42b.gif (436 bytes)

4

u3obj42c.gif (489 bytes)

9

u3obj42d.gif (519 bytes)

u3obj4-2.gif (1894 bytes)
(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

u3obj4-3.gif (2657 bytes)
(Notice that x cannot be equal to 0 because you
cannot divide by 0 and this graph is a function)


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