Cambridge International Mathematics

388 Introduction to functions (Chapter 19)

Example 3 Self Tutor

Which of these relations are functions?

abc

a Every vertical line we could draw cuts

the graph only once.

) we have a function.

b Every vertical line we could draw cuts

the graph at most once.

) we have a function.

c This vertical line

cuts the graph twice.

So, the relation is

not a function.

EXERCISE 19B.2

1 Which of the following sets of ordered pairs are functions? Give reasons for your answers.

a (1,1),(2,2),(3,3),(4,4) b (¡ 1 ,2),(¡ 3 ,2),(3,2),(1,2)

c (2,5),(¡ 1 ,4),(¡ 3 ,7),(2,¡3) d (3,¡2),(3,0),(3,2),(3,4)

e (¡ 7 ,0),(¡ 5 ,0),(¡ 3 ,0),(¡ 1 ,0) f (0,5),(0,1),(2,1),(2,¡5)

2 Use the vertical line test to determine which of the following are graphs of functions:

abc

de f

gh i

3 Will the graph of a straight line always be a function? Give evidence.

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