Question

classify each function as a power function, root function, polynomial (state the degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.
(a) ( f(x) = x^3 + 8x^2 )
power function
root function
polynomial of degree 2
polynomial of degree 3
rational function
exponential function
(b) ( g(t) = cos^2(t) - sin(t) )
power function
polynomial function
rational function
algebraic function
trigonometric function
exponential function
(c) ( h(t) = tsqrt{2} )
power function
root function
polynomial function of degree 2
rational function
algebraic function
exponential function
(d) ( v(t) = 9^t )
power function

Explanation:

(a) A polynomial function is a sum of monomials; the highest power (degree) is 3.
(b) The function uses trigonometric terms $\cos(t)$ and $\sin(t)$.
(c) A power function has the form $y=kt^n$ where $n$ is a constant; here $n=\sqrt{2}$.
(d) An exponential function has the variable in the exponent, here $t$ is the exponent of base 9.

Answer:

(a) polynomial function of degree 3
(b) trigonometric function
(c) power function
(d) exponential function