Find the domain of the following rational function write it

Question

Problem 1:

Find the degree, the leading term, the leading coefficient, the constant term and the end behavior of the given polynomial.

f (x) = 4x⁵ - x² + 2x + 5

Problem 2:

Find the domain of the following rational function. Write it in the form p(x)/q(x) for polynomial functions  p and  q  and simplify:

f (x) = 1 - {3 / (x + 1)

Problem 3:

Sketch a detailed graph of:

f(x) = 2x / (x² - 1)

Problem 4:

Perform the indicated operation and simplify

10x(x - 3)^-1 + 5x²(-1)(x - 3)^-2

Problem 5:

Solve the rational equation.

2x / (x + 3) = 5

Problem 6:

Let f (x) = x²  and g(x) = 1 + √x.  Find and simplify the indicated composite  function. Also, state the domain of the composite function.

(f ? g)(x)

Problem 7:

Graph the function and use the Horizontal Line Test to check if the function is one-to-one:

f (x) = x² - 2x + 2

Problem 8:

Perform the indicated operations and simplify:

³√(64x¹⁴)

Problem 9:

For the following function, state it domain and create sign  diagram:

f (x) = x√(x - 1)

Problem 10: Simplify the following:

log₂(1/64)