Chapter 1 Worked Examples: Functions

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Example 1:

Find the domain and range of these relations: 

a) {(1,4),(2,7),(3,10),(4,13)}

b) {(-2,4),(-1,1),(0,0),(1,1),(2,4)}


a) The domain is {1,2,3,4}

The range is {4,7,10,13}

b) The domain is {-2,-1,0,1,2}

The range is {0,1,4}

  • So the domain is the x value of a pair and the y value represents the range
  • Do not repeat value, eg even though in b) there are two 4s and two 1s

Example 2

Which of these sets of ordered pairs are functions?

a) {(1,4),(2,6),(3,8),(3,9),(4,10)}

b) {(1,3),(2,5),(3,7),(4,9),(5,11)}

c) {(-2,1),(-1,1),(0,2),(1,4),(2,6)}


a) Not a function because the number 3 appears twice in the domain 

b) A function because all of the elements are different 

c) A function because all of the elements are different.

  • It does not matter is there are y values which are the same 

Example 3

What are the graphical characteristics that a relation must have in order to be classified as a function?


Using the vertical line test, there must be no point at which it crosses the curve more than once. Therefore, there must be no point at which there are two y values for one x value. 

Example 4

Identify the horizontal and vertical asymptotes for these functions if they exist. 

a) y=2^x

b) y=2x/(x+1)

c) y=(x+2)/(x+1)(x-2)


  • This can be shown both graphically and by calculation. Graphically an asymptote is shown by the line which the curve tends towards but never reaches. Below I have shown these…


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