4. Is the length of
14
30
Pen
Pencil
Ruler
Needle
Stick
cm object
Here one amount is the length of many objects.
This is a ONE to MANY relationship
7. f : x x2
+4
f(x)=x2
+4
The upper function is read as follows:-
‘Function f such that x is mapped onto x2
+4
8. Lets look at some function
Type questions
If
f(x) = x2 + 4 and g(x) = 1 − x2
Find f(2)
Find g(3)
f(x) = x2
+ 42 2 = 8 g(x) = 1 − x2
3 3
= -8
9. Consider the function f(x) = 3x − 1 We can consider this as two simpler
functions illustrated as a flow diagram
Multiply by 3 Subtract 1
3x 3x − 1x
Consider the function f : x (2x + 5)2
x
Multiply by 2 Add 5
2x 2x + 5
Square
(2x + 5)2
10. f : x 3x + 2 and g(x) : x x2
Consider 2 functions
fg is a composite function, where g is performed first and then f is performed
on the result of g.
The function fg may be found using a flow diagram
x
square
x2
Multiply by 3
3x2
Add 2
3x2
+ 2
g f
Thus fg = 3x2
+ 2
12. Consider the function f(x) = 5x − 2
3
Here is its flow diagram
x
x5
x5 -2 f(x) = 5x − 2
3
Draw a new flow diagram in reverse!. Start from the right and go left…
Multiply by 5 Subtract 2 Divide by three
Multiply by threeAdd twoDivide by 5
x3x3x +23x +2
5
f−1
(x) = 3x + 2
5
And so
15. This powerpoint was kindly donated to
www.worldofteaching.com
http://www.worldofteaching.com is home to over a
thousand powerpoints submitted by teachers. This is a
completely free site and requires no registration. Please
visit and I hope it will help in your teaching.