Function Notation Worksheet With Answers printable pdf download

Function Notation Worksheet With Answers

Maths Learning Service: Revision

Mathematics IA

Function Notation

Mathematics IMA

A function is a rule for calculating a single value y = f (x) from an input value x. (Note:

“f (x)” does not mean “f

x”.)

Examples:

(1) Consider the rule y = f (x) = 2x + 3.

If x = 1

then f (1) = 2

1 + 3 = 5

If x =

3 then f ( 3) = 2

( 3) + 3 =

3 etc.

Recall that the points (x, y) or (x, f (x)) satisfying this rule lie on a straight line. We say

that the graph of the function f (x) = 2x + 3 is a straight line.

(2) Consider the rule f (x) = x + 2x.

Again recalling earlier work, we know that the graph of this function is a parabola.

If x = 1

then f (1) = 1 + 2

1 = 3

If x =

3 then f ( 3) = ( 3) + 2

( 3) = 3 etc.

(3) Function notation allows us to input algebraic symbols and formulae as well as numbers.

If f (x) = x

1, then

(a) f (a) = a

(b) f (x + h) = (x + h)

(c)

f (x ) = (x )

1 = x

(d) f ( x + 1) = ( x + 1)

1 = x

(4) Consider two functions f (x) = x and g(x) = x + 1. The following composite functions

can be formed

(a) f (g(x)) = f (x + 1) = (x + 1)

(b) g(f (x)) = g(x ) = x + 1

(d) g(g(x)) = g(x + 1) = (x + 1) + 1 = x + 2

Note: The concept of composite functions is useful for understanding the Chain Rule of

diﬀerentiation and inverse functions.

Function Notation Worksheet With Answers