Identifying Functions in Math

The mathematical concept of a function expresses the intuitive idea that one quantity (input) completely determines another quantity (output). A function assigns a unique value to each input of a specified type. The argument and the value may be real numbers, but they can also be elements from any given sets: the domain and the co domain of the function. (Source : WIKIPEDIA)


For example, f(x) = 3x2 .Here f(x) is a function that express three time the square of the number. In this article we are going to discuss about how to identifying the function.

Representation of functions in math:

The functions in math can be represented in four ways.

Verbal
Table of values
Numerical
Graphical

The functions in math can be identified by using the table of values,graphical and verbal statements.

Example for representation of functions:

1.Verbal representation :

The cool drinks that john get from the vending machine depends upon the code that he enter when provoked.

2.Table of values:

x             0             1             2               3                    4

y             3             7            11            15                 19

3. Numerical

f(x) = 4x+3

4.Graphical

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Fig(i) Graph of function

In the following section,  we are going to see how for identifying the function in math when we given the table of values.

Problems on identifying the function in math:

Problem 1:

Identifying the function for the following math table of values

x         -2           -1          0             1          2

y          8           -1          0             1          8

Solution:

Given   x         -2           -1        0             1          2

y          8            1          0             1          8

When we give x = -2 we get f(x) = y = 8 = x3

x = - 1 we get f(x) = y = -1 = x3

x = 0   we get f(x) = y = 0 = x3

x = 1   we get f(x) = y = 1 = x3

x = 2   we get f(x) = y = 8 = x3

So the function for given table of values id f(x) = y = x3

Answer: y = x3


Problem 2:

Identifying the function from the following verbal statements.

The cost for activate a device is 5000 per week It also costs 6 for each unit produced in the device. Identifying the function for daily cost x of run the device as a function of the number m of units produced.

Solution:

The   cost y equals the cost of $5,000 plus the cost of producing x units.

For 1 unit the cost is $6 .So for x units 6x

So the total cost y,

y = 5000 + 6 x

Answer: y  = 5000 + 6 x