Introduction
A function is a rule that is applicable for a variable, a table is used to list out all the out comes based on the given function. To understand a function first we need to understand about a variable and based on the function we can construct a table. A math function table is a table which is used to plot possible out comes of a function.
The important things that we need to note down for constructing a table are:
• Variables
• Function
• Outcomes
Variable
A variable is a value which we take up in unknown situations.
Example:
Suppose if we need to find out an area of a square we will write it as s2.
‘s’ is a variable here which refers to side of a square.
Function
A function is a set of order pairs where for every ‘x’ value there will be one ‘y’ value.
Example:
A function is always defined as y=f(x) where for every ‘x’ value there will be one exact value for ‘y’.
Outcome
Outcomes are the final results of the function.
Table
A table generally has number of rows and columns. Each element should be placed in blocks called as fields, and each field contains the values. Based on the values we can plot possible outcomes for a function.
For example consider an expression y=x3-3x2+4x-6
The table can be plotted as shown below:
| x | x3 | -3x2 | 4x | -6 | y |
| -2 | -8 | -12 | -8 | -6 | -34 |
| -1 | -1 | -3 | -4 | -6 | -14 |
| 0 | 0 | 0 | 0 | -6 | -6 |
| 1 | 1 | -3 | -4 | -6 | -4 |
In the above table we plotted all the possible out comes for the variables x, x3,-3x2, 4x and y.
Function tables
Function tables are the simple tables which provide the list of possible values of a variable and function. It mainly has 2 columns x and f(x).
It is constructed as shown below.
Consider an expression y=x+3, we write it as follow
x f(x)
-2 1
-1 2
0 3
1 4
2 5
In the above table we wrote the x value and f(x) value.
Solved Problems
1)Construct a table for the information given below:
Annual report:
The total population of the country - 3000000
The people who resides at rural area - 1300000
The people who reside at towns region - 900000
The total people who reside at cities – 600000
The total people who reside at metropolitan cities – 200000
The annual economies at all these regions are 28, 40, 47, and 60 (in crores).
Usages of natural resources are mentioned as 48% in rural areas, 26% in towns, 19% in cities and 7% in metropolitan cities.
Industries development is 16% 24% 28% and 32%
Development made in these regions is 22% 24% 26% 28%
ANS:The table is constructed for given data as shown below:
| Given | Rural | Town | Cities | Metroplotian |
| Population | 1300000 | 900000 | 600000 | 200000 |
| Economy | 28 | 40 | 47 | 60 |
| Natural | 48% | 26% | 19% | 7% |
| Industries | 16% | 24% | 28% | 32% |
| Development | 22% | 24% | 26% | 28% |
2)Construct a table for an equation y=x3+4x2-5x+4
Solution : Given equation, y=x3+4x2-5x+4
We are constructing table for given equation with different values.
| x | x3 | 4x2 | -5x | 4 | y |
| -2 | -8 | 16 | 10 | 4 | 22 |
| -1 | -1 | 4 | 5 | 4 | 12 |
| 0 | 0 | 0 | 0 | 4 | 4 |
| 1 | 1 | 4 | -5 | 4 | 4 |
Related Tags
Define Functions , Functions solved examples , What are Functions