Lesson Element – 6.05a Functions
Task 1 – Order of Operations
a)
Use the function diagram cards to build the function diagrams that generate each table of
input/output values.
b)
Express the function in algebraic form.

INPUT
x
May 2015
OUTPUT
y
+ 12
+6
×3
+2
-8
÷2
×4
×2
-4
+3

Input x
Output y
Input x
Output y
Input x
Output y
-4
-10
-4
4
-4
-4
-2
-4
-2
5
-2
4
0
2
0
6
0
12
2
8
2
7
2
20
4
14
4
8
4
28
Input x
Output y
Input x
Output y
Input x
Output y
-4
-2
-4
-13
-4
-20
-2
2
-2
-5
-2
-14
0
6
0
3
0
-8
2
10
2
11
2
-2
4
14
4
19
4
4
Input x
Output y
Input x
Output y
Input x
Output y
-4
1
-4
-6
-4
-16
-2
2
-2
0
-2
-12
0
3
0
6
0
-8
2
4
2
12
2
-4
4
5
4
18
4
0
May 2015
Task 2 – Inverse Functions Card Sort
a)
Match the functions to their correct table of input/output values.
b)
Pair the functions to their inverse functions.
x
-2
-1
0
1
2
y
-5
-2.5
0
2.5
5
x
-2
-1
0
1
2
y = 5x - 2
y=
x
-2
-1
0
1
2
x
-2
-1
0
1
2
y
0
5
10
15
20
y=
x
-2
-1
0
1
2
y=
May 2015
2x
5
y
-12
-7
-2
3
8
x +2
5
y
-9
-7
-5
-3
-1
x -2
5
y
-0.8
-0.6
-0.4
-0.2
0
x
-2
-1
0
1
2
y=
y=
x
-2
-1
0
1
2
x
-2
-1
0
1
2
y = 2x + 5
x
-2
5
x
-2
-1
0
1
2
y = 5x + 2
y
-0.8
-0.4
0
0.4
0.8
y
1
3
5
7
9
y
-3.5
-3
-2.5
-2
-1.5
x +5
2
y=
y
0
0.2
0.4
0.6
0.8
5x
2

x
-2
-1
0
1
2
y
1.5
2
2.5
3
3.5
y = 5( x + 2)
x
-2
-1
0
1
2
y=
x
-2
-1
0
1
2
y=
y
-8
-3
2
7
12
x -5
2
y
-2.4
-2.2
-2
-1.8
-1.6
x
+5
2
x
-2
-1
0
1
2
y
-14
-12
-10
-8
-6
y = 2x - 5
x
-2
-1
0
1
2
y
4
4.5
5
5.5
6
y = 2( x - 5)

The following function diagram cards can be used as a tool kit to build the function diagrams:
+2
×2
-2
÷2
×5
-5
+5
÷5
INPUT
x
OUTPUT
y
Extension
Draw your own function diagrams and their corresponding inverse function diagrams. Write down both
the original function and inverse function in algebraic form.
May 2015
Task 3 – Composite Functions
a)
Investigate which combinations of functions A to D will produce the eight tables of input/output
values given below – e.g. function ___ followed by function ___ gives table ___.
b)
Express the composite function in algebraic form.

Function A
+2
×3
Function B
Square
Function C
×2
+3
×6
+5
Function D
May 2015

x
0
1
2
3
4
5
y
4
25
64
121
196
289
x
0
1
2
3
4
5
y
8
17
26
35
44
53
x
0
1
2
3
4
5
y
3
5
11
21
35
53
x
0
1
2
3
4
5
y
13
25
37
49
61
73
x
0
y
7
x
0
y
11
1
2
3
4
5
13
19
25
31
37
1
2
3
4
5
17
23
29
35
41
x
0
1
y
0
1
x
0
1
y
17
35
2
3
16
81
2
3
53
71
4
5
256
625
4
5
89
107
Extension
Create two new function diagrams, E and F, and three new tables of input/output values for any
combination of functions A to F. Give these additional diagrams and tables to your classmates to
investigate.
May 2015