Basic Classes of Functions

Power functions and polynomials

Rational and algebraic functions

Transcendental functions

Combining functions

The polynomial p(x) = 3x^5 - 2x^2 + 1 has positive leading coefficient and odd degree. Which description of its end behavior is correct?

Which line is a vertical asymptote of the rational function f(x) = (2x + 1)/(x - 1)?

What is the domain of the natural logarithm function g(x) = ln(x - 3)?

With f(x) = sqrt(x) and g(x) = x - 4, which expression equals the composition (f composed with g)(x) = f(g(x))?

The temperature model T(t) = 10 sin((pi/12) t) + 15 has time t in hours. What are the amplitude and period of the oscillation?

Which of the following functions is transcendental rather than algebraic?

The polynomial p(x) = 4x^3 - x + 7 has what degree? Answer with a number.

The rational function f(x) = (2x + 1)/(x - 1) levels off at a horizontal asymptote. What is the y value of that asymptote? Answer with a number.

The function sin(4x) completes one full cycle when 4x grows by 2 pi. What is its period? Answer with a number.

With f(x) = x^2 and g(x) = x + 3, what number is (f composed with g)(1) = f(g(1))? Answer with a number.