Cambridge Additional Mathematics

Functions (Chapter 2) 41

So, fwould convert 2 into 2(2) + 3 = 7 and

¡ 4 into 2(¡4) + 3 =¡ 5.

This function can be written as:

f:x 7! 2 x+3

functionf such that xis converted into 2 x+3

Two other equivalent forms we use are f(x)=2x+3 and y=2x+3.

f(x)is the value ofyfor a given value ofx,so y=f(x).

fis the function which convertsxintof(x), so we write

f:x 7 !f(x).

y=f(x) is sometimes called thefunction valueorimageofx.

For f(x)=2x+3:

² f(2) = 2(2) + 3 = 7.

) the point(2,7)lies on the graph of the function.

² f(¡4) = 2(¡4) + 3 =¡ 5.

) the point(¡ 4 ,¡5)also lies on the graph.

Alinear functionis a function of the form f(x)=ax+b wherea,bare real constants.

The graph of a linear function is a straight line.

Example 3 Self Tutor

If f:x 7! 2 x^2 ¡ 3 x, find the value of: a f(5) b f(¡4)

f(x)=2x^2 ¡ 3 x

a f(5) = 2(5)^2 ¡3(5)

=2£ 25 ¡ 15

=35

freplacingxwith(5)g

b f(¡4) = 2(¡4)^2 ¡3(¡4)

= 2(16) + 12

=44

freplacingxwith(¡4)g

EXERCISE 2B

1 If f(x)=3x¡x^2 +2, find the value of:

a f(0) b f(3) c f(¡3) d f(¡7) e f(^32 )

2 If g:x 7 !x¡

4

x

, find the value of:

a g(1) b g(4) c g(¡1) d g(¡4) e g(¡^12 )

fx

fx

()is read as

“of ”.

y

x

f(x) = 2x + 3

(2 7),

(-4 -5),

O

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_02\041CamAdd_02.cdr Thursday, 5 December 2013 9:19:38 AM GR8GREG