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Example 14 from Precalculus, 1.1 Functions and Function Notation
Applying the Vertical Line Test
Which of the graphs in Figure 12 represent(s) a function
Figure
12
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
If any vertical line intersects a graph more than once, the relation represented by the graph is not a function. Notice that any vertical line would pass through only one point of the two graphs shown in parts (a) and (b) of Figure 12. From this we can conclude that these two graphs represent functions. The third graph does not represent a function because, at most x-values, a vertical line would intersect the graph at more than one point, as shown in Figure 13.
Figure 13
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Does the graph in Figure 14 represent a function?
Figure
14
How did it go?