# Functions

Document Sample

```					  Functions

►Defining a function
►Using function notation
►Matching functions to graphs
What is a function?
►Arule or a process which gives EXACTLY
ONE output for EVERY input.

Input        Function                       Output

In order for this to be defined as a
function, there must only be one
unique possibility for this output.
What is a function?
► Isy = 3x + 2 a function?
► Lets try x = 6 as our input

6           3x + 2         20

►No   matter what value we would have
used for our input, the output would
have been unique. Therefore it can be a
rule for a function.
What is a function?
► Isy = +-x a function?
► Lets try x = 4 as our input

4            x             2 or -2

►Positive input values always give two
solutions and negative values would give
no solutions so y = +-x is not a rule for
a function.
Activity 1
Time allowed – 5 minutes

►Turn to page 6 of your Core 3
A2 and A3
Defining a function
► Thedefinition of a function consists of two
parts:

The Rule   How function is calculated
The Domain Set of values which rule is
applied to
The Domain
► When  defining a function you MUST specify
the set of input values to be used (domain).

► Ifthe domain is omitted we assume the
function is defined for all values.
The Domain
► Y=x    generates one value of y for all inputs
greater than or equal to 0.
► If x is negative we get no solution. So this,
on it’s own, would not give a function.
► However, if we state that the domain is the
set of values where x ≥ 0, we can now
define this as a function.
The Rule
► We   usually use letters to stand for
functions, commonly f, g or h.
► If we call the square root function f, we can
write it as.
► f (x) = x , x ≥ 0

Rule                Domain
Putting into context..
► The  context of a question can sometimes
restrict the domain.
► g (x) = x3 can be defined for all values.
► If the above was applied to finding the
volume of a cube of side x, then it wouldn’t
be appropriate to include negative values in
our domain.
Activity 2
Time allowed – 3 minutes

►Turn to page 8 of your Core 3
Graphing a function
Sketch the graph of y = f (x) where f (x) = x2 - 2 , x ≥ -2

Shown for all real values               Shown for f (x), where
of x.                                   x ≥ -2. Why is there a
closed circle at (-2,2)?
Notation
means ‘x belongs to the set of
real numbers’

Can also be written
Activity 3
Time allowed – Rest of lesson

►Turn  to page 9 of your Core 3