1. What is the end behavior of the polynomial function $f(x) = 4x + 7x^5 - 2x^2$?
2. Which statement describes the end behavior of the function $g(x) = -3x^4 + 5x^3 - x + 9$?
3. A polynomial function $p(x)$ has an odd degree. Its graph rises to the left and falls to the right. The sign of its leading coefficient must be ___.
4. For the polynomial $h(x) = -2x^7 + x^4 - 8$, what is the behavior of $h(x)$ as $x$ approaches negative infinity ($x \to -\infty$)?
5. Consider the function $f(x) = 10 - 4x^6 + 3x$. As $x \to \infty$, $f(x)$ approaches ___. (Use $\infty$ or $-\infty$)
6. The height of a model rocket in feet is given by $h(t) = -16t^2 + 128t$, where $t$ is the time in seconds after launch. What is the most reasonable domain for this function?
7. A company's daily revenue $R(x)$ from selling $x$ handmade chairs is modeled by a polynomial. The company can produce at most 75 chairs per day. Which interval represents the practical domain for $x$?
8. An open-top box is made by cutting identical squares of side length $x$ from the corners of a 10-inch by 18-inch sheet of cardboard. Which inequality represents the practical domain for $x$?
9. The volume of a box made from a 24-inch by 36-inch piece of metal is $V(x) = x(36-2x)(24-2x)$. The domain for the cut length $x$ is $0 < x < b$. What is the value of $b$? ___
10. A polynomial function $P(n)$ models the population of a bacterial colony after $n$ hours. Which of the following is the most fundamental restriction on the domain for $n$?