Form 4 & 5 Unit 1 Lesson 1 – Introduction to functions

Objectives

At the end of the lesson, students should be able to;

• Use notation to describe simple functions.
• Find the value of the function at some point.
• Write down an expression for the function when given different values of x.
• Find the value of x, when two functions are equal
• Find the value of x, when given the equivalent value of the function.

An expression in the form 3x – 2, in which the variable is x is considered “a function of x”. The numerical value of the expression depends on the value of x. This expression can also be written as

Example 1

If f(x) = 4x + 2, find the value of f (2) and f (-3).

Solution

We use simple substitution of x for the values 2 and -3.

f (2) implies that the value of x is given as 2. We substitute the value of x into the expression f (x)= 4x + 2 to find the corresponding output.

f(x) = 4x + 2

f(2) = 4(2) + 2

= 8 + 2

= 10

Substituting -3 into the expression will give us the result below.

f (-3) = 4(-3) + 2

= -12 + 2

= –10

Example 2

If f(x) = 5 – 2x, find the value of f (3) and f (-3).

Solution

Substitute 3 into the expression.

f (x) = 5 – 2x

f (3) = 5 – 2(3)

= 5 – 6

= -1

Substitute -3 into the expression f(x)= 5-2x.

f (-3) = 5 – 2 (-3)

= 5 + 6

= 11

Example 5

There are instances where numbers are not given for substitution but instead algebraic expressions.

If f(x) = x + 2, simplify

1) f ( 2x+5)

2) f ( x ) – 4x

3) f( ³/₂ x + 10 )

Example 6

There are instances where you will be asked to solve a linear equation.

If f(x) = 6x +16 and f(x) =10, solve for x.

Solution

f(x) = 6x + 16   and   f(x) = 10

Substitute f(x) =10 into f(x) = 6x + 16

10 = 6x + 16

10 – 16 = 6x

– 6 = 6x

x=-1