Unit 2 test: Polynomial and Rational Functions

Which describes the end behavior of $f(x) = 4x^3 - x^6 + 2$?

For $f(x) = x^2(x - 3)^3(x + 1)$, at which zero does the graph touch the $x$-axis and turn back?

The polynomial $f(x) = a(x - 1)(x + 2)^2$ passes through the point $(2, 32)$. Find $a$.

For $f(x) = x^3 + 2x - 5$, which interval is guaranteed by the intermediate value theorem to contain a zero?

Find all zeros of $f(x) = 3x^3 - 4x^2 - 5x + 2$.

Find all zeros of $f(x) = x^3 - 4x^2 + x + 2$. Use sqrt() for square roots.

What does Descartes' rule of signs tell you about the positive real zeros of $f(x) = 2x^4 + x^3 + 5x + 1$?

The polynomial $f(x) = x^3 - 3x^2 + 4x - 2$ has one real zero and two non-real zeros $a \pm bi$ with $b > 0$. Enter $(a, b)$.

Given that $-i$ is a zero of $f(x) = x^4 + 2x^3 - 2x^2 + 2x - 3$, find all the real zeros of $f$.

The graph of $f(x) = \dfrac{x^2 - 3x}{x^2 - 9}$ has a hole. Give its coordinates.

Find the slant asymptote of $f(x) = \dfrac{x^2 + 5x + 2}{x + 1}$. Enter it as $y = \ldots$

The graph of $f(x) = \dfrac{2x^2 + x}{x^2 - 4}$ crosses its horizontal asymptote at one point. What is its $x$-coordinate?

Solve $x^3 + 2x^2 - 15x < 0$.

Solve $\dfrac{x + 2}{x - 4} \ge 3$.

Solve $\dfrac{(x - 1)^2(x + 2)}{x - 3} \le 0$.