Unformatted text preview: t of x being a function of y . In this
case, R1 represents x as a function of y ; R2 does not. 1.4 Introduction to Functions 35 It is worth taking some time to meditate on the Vertical Line Test; it will check to see how well
you understand the concept of ‘function’ as well as the concept of ‘graph’.
Example 1.4.2. Use the Vertical Line Test to determine which of the following relations describes
y as a function of x.
y y 4 4 3 3 2 2 1 1 1 2 3 x −1 −1 x 1
−1 The graph of R The graph of S Solution. Looking at the graph of R, we can easily imagine a vertical line crossing the graph
more than once. Hence, R does not represent y as a function of x. However, in the graph of S ,
every vertical line crosses the graph at most once, and so S does represent y as a function of x.
In the previous test, we say that the graph of the relation R fails the Vertical Line Test, whereas
the graph of S passes the Vertical Line Test. Note that in the graph of R there are inﬁnitely many
vertical lines which c...
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