Exam 3: Polynomial and Rational Functions

Provide an appropriate response. -Let P be a polynomial function with real coefficients. If -3, 10, -3 + 8i, and 7 - 6i are zeros of P, what is the smallest possible degree that P can have?

Identify the vertex of the parabola. -f(x) = - - 6

Discuss the symmetry of the graph of the polynomial function. -f(x) =

Use the rational zero theorem, Descartes's rule of signs, and the theorem on bounds as aids in finding all real and imaginary roots to the equation. - + 9x + 27 = 0

Describe the behavior of the function's graph at its x-intercepts. -

For the given function, find all asymptotes of the type indicated (if there are any). -f(x) = , oblique

Solve the absolute value equation. -

Use synthetic division to find the quotient and remainder when the first polynomial is divided by the second. -

Graph. -

For the given function, find all asymptotes of the type indicated (if there are any). -f(x) = , horizontal

Find all real and imaginary solutions to the equation. -

Use the leading coefficient test to determine whether . -y =

For the given function, find all asymptotes of the type indicated (if there are any). -f(x) = , horizontal

Find all of the real and imaginary zeros for the polynomial function. -f(x) =

Find all real and imaginary solutions. - - 16 = 0

Sketch the graph of the polynomial function. -

Find all of the real and imaginary zeros for the polynomial function. -f(x) =

Explain the behavior of the graph of f(x) as it approaches its vertical asymptote. -f(x) =

Use Descartes's rule of signs to discuss the possibilities for the roots of the equation. Do not solve the equation. -

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - - 20x + 20; x - 2