1. A function is a rule that maps a single number to another single number
Functions can be written in different ways
y = 2x + 3
f(x) 2x + 3
f : x 2x + 3
Using the function f (x) x2 ,
one number input gives one number output
However, the function f (x)
one input number gives 2 outputs and is
therefore not a function
When plotting on axes the vertical axis is labelled f (x) or f : x not y

2. Determine which of these mappings are functions:
Qwertyuiiop[]#’;’
Determine which of these mappings are functions:
f(x) ’2x - 3
FUNCTION
NOT A FUNCTION
FUNCTION
NOT A FUNCTION
f(x)’ 1
x - 1
FUNCTION
NOT A FUNCTION
f(x) ’
FUNCTION
NOT A FUNCTION
f(x)’ x2 + 3
FUNCTION
NOT A FUNCTION
f(x) ’ the greatest integer less than or equal to x
FUNCTION
NOT A FUNCTION
f(x)’ the height of a triangle whose height is x
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3. Correct
Return

4. WRONG!!!
Return

5. Translating Functions
Principles
If y = x is the function f(x) x
Then f(x) + 3
is the function f(x) x + 3 1 3 4 5 2 7 6
- 7 -1 -3 -4 -5 -2 -6 -7 1 3 4 5 2 7 6
- 7 -1 -3 -4 -5 -2 -6 -7
y = x + 3
f( x) + 3
y = x
f( x)
We have seen from the equations of
straight lines that from the general
equation y = mx + c, the integer c has an effect
on where a straight line crosses the y axis
So the adding or subtracting of an integer
translates the graph up or down
f(x) 1 3 4 5 2 7 6
- 7 -1 -3 -4 -5 -2 -6 -7 1 3 4 5 2 7 6
- 7 -1 -3 -4 -5 -2 -6 -7
f(x) + 3
This is the same for any function
This can also be described
as a translation

6. Translating Functions
Principles
There are other translations that can be performed on graphs:
y = x2
y = (x-2)2
The equation (x – 2)2 = 0 has root x = 2
Compare the equation y = (x – 2)2
with the graph y = x2 2
This can also be described
as a translation
So to summarise these two translations:
The graph of y = f (x) + a is the graph of y = f(x) translated by
The graph of y = f (x - a) is the graph of y = f(x) translated by

7. Stretching Functions We will use the sine wave as an example y = sinx
Now see what happens when we double the function y =2 x sinx
or more precisely written y =2sinx
The graph is stretched to twice its size in the x direction
Now see what happens when we double the x value before finding the sine y =sin (2 x x)
The graph is squashed to half its size in the y direction
or more precisely written y =sin2x

8. Summary Graph Description Translation
Graph
Description
Translation
Stretch by a scale factor a parallel to the y axis
Stretched by scale factor parallel to the x axis
Reflection in the x axis of
Reflection in the y axis of