Determine whether the function is a polynomial function. If it is, state the degree. If it is not, tell why not.
g(x)= (7-x^2)/2

Question

Determine whether the function is a polynomial function. If it is, state the degree. If it is not, tell why not.
g(x)= (7-x^2)/2

mathstudent55 · Answer

A polynomial function has one ore more terms. A term is made up of a number, called coefficient, and a variable part. The variable part can have no variable or one or more variables raised to positive, integer exponents.

anonymous · Answer

so it not a polynomial because of the negative coefficient of x^2

mathstudent55 · Answer

g(x) = (7 - x^2)/2
g(x) = 7/2 - (1/2)x^2
Now you see clearly two terms.
The first term is simply a number. That is fine for a polynomial function.
The second terms is (1/2) (a number or coefficient) multiplied by a variable, x, raised to a positive integer power. So it is a polynomial function.

anonymous · Answer

so the polynomial function would be 2 or 7?

anonymous · Answer

it is a polynomial because even though it is a negative coefficient it still has a variable to a certain degree which in this case is a degree of 2 or x^2

mathstudent55 · Answer

It is a polynomial function. Now the degree.
The degree of a term is the sum of all exponents of the variables of that term. The degree of a polynomial is the same as the degree of its highest term.

anonymous · Answer

The degree is the highest exponent, for example x^1  has a degree of 1 and (-1/2)x^2 has a degree of 2 because the exponent is 2, the degree of the entire function is the highest degree of all the variables in that function in  this case the function g(x) has a degree of 2 because the highest exponent is 2

anonymous · Answer

okay thank you!!!

anonymous · Answer

np