For the following problem, find the real zeros (if any) of the polynomials.

$$y=x^4+6 x^2+9$$

The given figure shows the cost function, C(n), from the previous problem, and a line, $l$, that passes through the origin.

(a) What is the slope of line $l$?

(b) How does line $l$ relate to $a\left(n_0\right)$, the average cost of producing $n_0$ units?

For the following problem, find the real zeros (if any) of the polynomials.

$y=a x^2\left(x^2+4\right)(x+3)$, where $a$ is a nonzero constant.

Write $y=3\left(\frac{2}{5 \sqrt{7 x}}\right)^4$ in the form $y=a x^p$ and state the values of a and p.

Is the statement in the following problem true or false? Give an explanation for your answer.

Let $g(x)=x^p$. If $p$ is a positive, even integer, then the graph of $g$ passes through the point $(-1,1)$.

For the following exercise, perform the operations. Express answers in reduced form.

$$\dfrac{1}{2 x}-\dfrac{2}{3}$$

Describe the behavior of y=x$^{-3}$ and y=x$^{1 / 3}$ as

(a) $x \rightarrow 0$ from the right

(b) $x \rightarrow \infty$

For the following problem, find the real zeros (if any) of the polynomials.

$$y=4 x^2-1$$

In the following exercise, simplify, if possible.

$$\frac{(w+2) / 2}{w+2}$$

For the polynomials in the following exercise, state the degree and the number of terms, and describe the long-run behavior.

$$y=2 x^3-3 x+7$$

Describe the behavior of y=x$^{-10}$ and y=-x$^{10}$ as

(a) $x \rightarrow 0$

(b) $x \rightarrow \infty$

(c) $\quad x \rightarrow-\infty$

Can the formula in the following exercise be written in the form of an exponential function or a power function? If not, explain why the function does not fit either form.

$$q(x)=5^{\left(x^2\right)}$$

What is the long-run behavior of the functions in the following problem?

$$y=\frac{x(x+5)(x-7)}{4+x^2}$$

In the following exercise, simplify, if possible.

$$\frac{1 /(x+y)}{x+y}$$