Calculus, 8th Edition,stewart; page 33 problem 1

Question

Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

(a) f(x) = log₂(x)      (b) g(x) = ∜x      (c) h(x) = 2x^3/(1 - x^2)      (d) u(t) = 1 - 1.1t + 2.54t^2                     

(e) v(t) = 5^t     (f) w(θ) = sin θ cos^2 θ

Answer 1

Step:1

(a)

The function is .

The function is in the form of  is a logarithmic function, where  is a positive constant.

The function  is a logarithmic function.

Step:2

(b)

The function is .

The function is in the form of  is a root function, where  is a positive integer.

The function  is a root function. 

Step:3

(c)

The function is .

The function is in the form of  is a rational function, where  and  are the polynomials.

The function  is a rational function.

Step:4

(d)

The function is .

The function is in the form of  is a polynomial function of degree 2.

The function  is a polynomial function of degree 2.

Step:5

(e)

The function is .

The function is in the form of  is an exponential function, where  is a positive constant.

The function  is an exponential function. 

Step:6

(f)

The function is .

The function contains the trigonometric functions.

The function  is a trigonometric function.

Solution:

(a) Logarithmic.

(b) Root.

(c) Rational.

(d) Polynomial with degree 2.

(e) Exponential.

(f) Trigonometric.