In the equation of a circle, both x and y are squared.
A
a
Polynomial, see solution.
B
b
Not a polynomial, see solution.
C
c
Polynomial, see solution.
D
d
Polynomial, see solution.
E
e
Not a polynomial, see solution.
Practice makes perfect
a
Polynomials are expressions that can be written as a sum of terms of the following form.
(any number)* x^((whole number))A parabola shows the graph of a second degree function and can generally be written in the following format.
f(x)=ax^2+bx+c
By rewriting some of the terms, we notice that they all follow the description of a polynomial.
( any number)* x^(( whole number))
↓
f(x)= ax^2+ bx^1+ cx^0
Therefore, parabolas are polynomial functions.
f(x)=ab^x
In exponential functions, the variable is in the exponent of a power. Therefore, exponential functions do not follow the description of a polynomial.
c
Cubics show the graph of a third degree function, and can generally be written in the following format.
f(x)=ax^3+bx^2+cx+d
By rewriting some of the terms, we notice that they all follow the description of a polynomial.
( any number)* x^(( whole number))
↓
f(x)= ax^3+ bx^2+ cx^1+ dx^0
Therefore, cubics are polynomial functions.
d
Lines shows the graph of a first degree function and can generally be written in the following format.
f(x)=mx+b
By rewriting some of the terms, we notice that they all follow the description of a polynomial.
( any number)* x^(( whole number))
↓
f(x)= mx^1+ bx^0
Therefore, lines are polynomial functions.
e
Circles can generally be written in the following format.
(x-a)^2+(y-b)^2=r^2
The equation of a circle does not follow the description of a polynomial.
