a) rational

b) rational

c)exponential

d) power function

e) polynomial function of degree 6

f) trig function

Step-by-step explanation:

Functions can be classified by the operations they contain. Remember the following functions:

Power function has as its main operation of an exponent on the variable.Root function has as its main operation a radical.Log function has as its main operation a log.Trig function has as its main operation sine, cosine, tangent, etc.Rational exponent has as its main function division by a variable.Exponential function has as its main operation a variable as an exponent.Polynomial function is similar to a power function. It has as its main function an exponent of 2 or greater on the variable.

Below is listed each function. The bolded choice is the correct type of function:

(a) y = x − 3 / x + 3 root function logarithmic function power function trigonometric function rational function exponential function polynomial function of degree 3

(b) y = x + x2 / x − 2 power function rational function algebraic function logarithmic function polynomial function of degree 2 root function exponential function trigonometric function

(c) y = 5^x logarithmic function root function trigonometric function exponential function polynomial function of degree 5 power function

(d) y = x^5 trigonometric function power function exponential function root function logarithmic function

(e) y = 7t^6 + t^4 − π logarithmic function rational function exponential function trigonometric function power function algebraic function root function polynomial function of degree 6

(f) y = cos(θ) + sin(θ) logarithmic function exponential function root function algebraic function rational function power function polynomial function of degree 6 trigonometric function