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Example 14 from Algebra and Trigonometry, 3.1 Functions and Function Notation
Applying the Vertical Line Test
Which of the graphs in Figure 9 represent(s) a function
Figure
9
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 9. 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 10.
Figure 10
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 11 represent a function?
Figure
11
How did it go?