Graph the function in the given viewing window. Then determine the domain and the range.

$f(x)=x^4-2 x^2-7, \quad[-4,4,-9,9]$

Factor each polynomial completely. If the polynomial is prime say so.

$$9 w-w^3$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Because I know how to clear an equation of fractions, I decided to clear the equation 0.5x+8.3=12.4 of decimals by multiplying both sides by 10.

Factor the polynomial completely. If a polynomial is prime, say so.

$$3 a^2-27 a$$

In the summer we like to write to people we know and let them know what we are doing. Complete the following sentences with the appropriate forms of écrire and dire.

Cecile et Melanie $\rule{1cm}{1pt}$ a leurs parents.

Elles leur qu'elles sont tres contentes de leurs vacances.

Comenta sobre las cosas que te rodean. Contrasta las cosas que están cerca de ti con las que están más lejos. Utiliza adjetivos demostrativos para mostrar las diferencias o las semejanzas que notas.

Modelo:

Este libro de texto es para mi clase de biología. Ese libro que tiene Pablo es para la clase de Ingles.

Aquella muchacha allá lleva más libros que nosotros. Aquellos libros son más pesados que estos libros.

Identify the incorrect verb form in each of the following sentences, and then provide the correct verb form.

EXAMPLE:The brothers had ran all the way to the ballpark before they found out that the game had been canceled.

ran-run

Alberto must have rode by that store a hundred times without noticing it.

Consider the function f(x) = 1/2 (ax)² - ax, a ≠ 0. (a) Determine the changes (if any) in the intercepts, extrema, and concavity of the graph of f when a is varied. (b) In the same viewing window, use a graphing utility to graph the function for four different values of a.

Find the temperature u(t, x) in a rod modeled by the initial/boundary value problem

$$\begin{aligned} u_{t}(x, t) &=k u_{x x}(x, t), \quad \mathrm { for } \ t>0 \ \mathrm { and } \ 0<x<L, \\ u_{x}(0, t) &=u_{x}(L, t)=0, \quad \mathrm { for } \ t>0, \\ u(x, 0) &=f(x), \quad \mathrm { for } \ 0 \leq x \leq L \end{aligned}$$

with the indicated values of the parameters. Plot the solution for a number of time values like those in the text that show the significant portion of the change of the temperature. Give a physical explanation of what is happening to the solution as time progresses. k=1, L=1, and $f(x)=\cos (\pi x)$

Express $\tan \theta$ in terms of $\csc \theta$.

Find the temperature u(t, x) in a rod modeled by the initial/boundary value problem

$$\begin{aligned} u_{t}(x, t) &=k u_{x x}(x, t), \quad \mathrm { for } \ t>0 \ \mathrm { and } \ 0<x \times L, \\ u(0, t) &=T_{0} \quad \mathrm { and } \ u(L , t)=T_{L}, \quad \mathrm { for } \ t>0, \\ u(x, 0) &=f(x), \quad \mathrm { for } \ 0 \leq x \leq L, \end{aligned}$$

with the indicated values of the parameters. k=2, $L=\pi$, $T_{0}=0$, $T_{L}=0$, and $f(x)=\sin 2 x-\sin 4 x$

Use a graphing utility to graph the three functions in the same viewing window. Describe the graphs of g and h relative to the graph of f.

$$\begin{array}{l}{f(x)=x^{3}-3 x^{2}+2} \\ {g(x)=-f(x)} \\ {h(x)=f(2 x)}\end{array}$$

The Central Limit Theorem defines large samples as having at least 36 elements.

True or false?

Write the equation $2 x^2-0.3 x=9$ in the standard form $a x^2+b x+c=0$ and give possible values of $a, b, c$. Note that there may be more than one possible answer.