Function where f is a polynomial is a polynomial function

It is of the form

f:
**
R → R
**

f(x) = a
_{
0
}
+ a
_{
1
}
x + a
_{
2
}
x
^{
2
}
+ …… + a
_{
n
}
x
^{
n
}
,

where n is a non-negative integer (i.e. n is 0, 1, 2, 3, ….)

and a
_{
0
}
, a
_{
1
}
, a
_{
2
}
, a
_{
3
}
…. a
_{
n
}
∈
**
R
**
, i.e. a
_{
0
}
, a
_{
1
}
, a
_{
2
}
, a
_{
3
}
…. a
_{
n
}
are all real numbers

Example

f(x) = x
^{
3
}
– 3x
^{
2
}
+ 4x + 2

f(x) = x
^{
19
}
– 81

Let us look at some common polynomial functions like