# Topic 6.05a Lesson element - Functions - Student worksheet

```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
&times;3
+2
-8
&divide;2
&times;4
&times;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
&times;2
-2
&divide;2
&times;5
-5
+5
&divide;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
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
&times;3
Function B
Square
Function C
&times;2
+3
&times;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
```