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What are Functions?

Updated: May 2


In this post you will be able to learn about functions, notations of functions and vertical line test. All points are inter-related to each other and mainly functions. By the end of the post you will be able to determine functions and know how to find the value of a function.


Functions is a relation in which a set of inputs have a set of outputs or A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output ( y ) with each input ( x ).

f of x

Notation of Functions


Here, y = output

x = input

While, f = Name of the function

Is the below relation a function or not?

Relation ={(1, 3), (2, 3), (3, 3)}

Yes this relation is a function because there is not repetition in domain.

Vertical Line Test

This is a type of graphical test in which a curve is determined whether it is a function or not. In this test a vertical line is drawn across the curve if it intersect the curve on one point it means the curve is a function and if the line intersect two times then it is not a function. Below are the given examples.

function or not

As it can be seen that circle is touched two times by the vertical line so it is not a function while the other line is intersected only once which means its a function. Below is another example given which illustrates functions and non-functions graphically.


Value of a Function

Now we will determine value of a function so below is the given equation.


Find, f(4) = ?


f(4) = 4^4 - 8(4) + 14

f(4)= 16 - 32 + 14

f(4) = -2


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