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# Introduction to function

Functions provide us with a convenient way to handle the relationship between the values of one variable quantity that depends on the values of another variable quantity.

Example :let us imagine a spherical rubber balloon into which air is being pumped. The radius o the balloon (r) is changing with time t. in mathematics, we say that r is a function of time t and symbolically, it may be written,

Similarly the volume of the balloon also depends on time t. hence we can write

Different letters  and  are used because they represent different mathematical relations.

In general, if the values of a variable  depend on the values of another variable , we write

i.e.,  is a function of.

represents some expression of

# Independent and Dependent Variables

In the function, is an expression in terms of. Here is known as the independent variable as  can take any number in functions domain. (whose values depend on ) is known as dependent variable as for a value of  it has a defined set of values. Thus  depends on  and therefore is called as dependent variable.