For each function, determine whether it is a polynomial function.Function Is the function a polynomial?Yes No=fx+9x2−5x7x (a) =fx+9x2−5x7x=gx5x7 (b) =gx5x7=ux+8x90.9x5 (c) =ux+8x90.9x5=vx−7 (d) =vx−7
Question
For each function, determine whether it is a polynomial function.Function Is the function a polynomial?Yes No=fx+9x2−5x7x (a) =fx+9x2−5x7x=gx5x7 (b) =gx5x7=ux+8x90.9x5 (c) =ux+8x90.9x5=vx−7 (d) =vx−7
Solution
(a) The function f(x) = x + 9x^2 - 5x^7 is a polynomial. This is because it is a sum of terms, each of which is a nonnegative integer power of x.
(b) The function g(x) = 5x^7 is also a polynomial. It is a single term, which is a nonnegative integer power of x.
(c) The function u(x) = x + 8x^9 - 0.9x^5 is a polynomial. Despite the coefficient being a decimal, it is still a sum of terms, each of which is a nonnegative integer power of x.
(d) The function v(x) = -7 is a polynomial. It is a constant function, which is a polynomial of degree 0.
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