For the following exercise,

With the use of a graphing utility, use numerical or graphical evidence to determine the left- and right-hand limits of the function given as $x$ approaches $a$. If the function has limit as $x$ approaches $a$, state it. If not, discuss why there is no limit.

$$f(x)=\left\{\begin{array}{ll}|x|-1, & \text { if } x \neq 1 \\ x^3, & \text { if } x=1\end{array} \quad a=1\right.$$

Solve the equation/inequality. Write the solution sets to the inequality in interval notation if nossible.

$$3-4\{x-5[x+2(3-2 x)]\}=-2[4-(x-1)]$$

Selye's concept of the general adaptation syndrome did not include ___________________.

A mi me gustan el queso y la salsa de tomate. Yo...

How were Daisy and Tom acting at Gatsby's party?

Write the equation of each graph after the indicated transformation(s). The graph of $y=x^2$ is translated five units to the right.

Find the first five terms of the sequence described.

$$a_1=-3, a_2=2, a_{n+1}=a_{n-1}-$$

$\overline{D E}$ has vertices D(1,3) and E(3,-3). Graph $\overline{D E}$ and its image after the indicated transformation.

Translation: along $\langle$ -2,-1 $\rangle$ Rotation: $270^{\circ}$ about the origin

Which pairs of functions below are inverse functions? Choose all that apply. A. $f(x)=\frac{x+2}{2} \text { and } f(x)=\frac{y+2}{2}$ B. $f(x)=3 x+9 \text { and } f(x)=\frac{1}{3} x-3$ C. $x=\frac{\sqrt{y}}{2} \text { and } 2 x^{2}=y$ D. $x=\frac{\sqrt{y}}{2} \text { and } 2 y^{2}=x$ E. $3 x-3=y \text { and } y=\frac{x+3}{3}$ F. $3 x-3=y \text { and } y=\frac{x-3}{3}$

Consider Method A compared to Method B in both the columns of the table given below.

Brody says $x \neq 0$ for the equation in the table, $\frac{2 x}{15 x^2} \cdot \frac{5 x^2}{8}=\frac{1 x}{12}$. Damiere says that there are no restrictions because the answer is $\frac{x}{12}$ and there are no variables in the denominator. Who is correct? Explain your reasoning.

$$\begin{aligned} \frac{2}{15} \cdot \frac{5}{8} & =\frac{10}{120} \\ & =\frac{1}{12}\end{aligned}$$

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$$\begin{aligned} \frac{2 x}{15 x^2} \cdot \frac{5 x^2}{8} & =\frac{10 x^3}{120 x^2} \\ & =\frac{1 x}{12}\end{aligned}$$

| |Method B | $\frac{\stackrel{1}{\cancel{2}}}{\stackrel{\cancel{15}}{3}} \cdot \frac{\stackrel{1}{\cancel5}}{\stackrel{\cancel8}{4}}=\frac{1}{12}$ | $\frac{\stackrel{1}{\cancel{2x}}}{\stackrel{\cancel{15x^2}}{3}} \cdot \frac{\stackrel{1}{\cancel{5x^2}}}{\stackrel{\cancel8}{4}}=\frac{1x}{12}$|

Complete each statement. $\$ 3 / \mathrm{lb}=\boldsymbol{\square} \cancel{c} / \mathrm{oz}$

The Populist Party of the 1890s was an example of a party formed chiefly to help __________.

a) a candidate register in a national election

b) a land area achieve statehood

c) a specific group of people

For the following exercise, solve the system for x, y, and z.

$$\begin{array}{r} x+y+z=3 \\ \frac{x-1}{2}+\frac{y-3}{2}+\frac{z+1}{2}=0 \\ \frac{x-2}{3}+\frac{y+4}{3}+\frac{z-3}{3}=\frac{2}{3} \end{array}$$

Analyze the examples shown in the table.

a. Explain the process for dividing rational expressions.

b. In Example 2, explain why $\frac{1}{4 a}$ is the multiplicative inverse of 4a.

$$\begin{aligned} \frac{1}{5}\div\frac{3}{10} & =\frac{1}{\stackrel{\cancel5}{1}} \cdot \frac{\stackrel{2}{\cancel{10}}}{3} \\ & =\frac{2}{3}\end{aligned}$$

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$$\begin{aligned} & \frac{x y^2}{5 z} \div \frac{3 x y}{10 z^2}=\frac{\stackrel{y}{\cancel{x y^2}}}{\cancel{5 z}} \cdot \frac{\stackrel{2z}{\cancel{10 z}}}{3\cancel{xy}} \\ & =\frac{2 y z}{3} ; x, y, z \neq 0 \\ & \end{aligned}$$

| Example 2|

$$\begin{aligned} \frac{6}{7}\div4 & =\frac{\stackrel{3}{\cancel6}}{7} \cdot \frac{1}{\stackrel{\cancel4}{2}} \\ & =\frac{3}{14}\end{aligned}$$

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$$\begin{aligned} \frac{6 a^3}{7 b} \div 4 a & =\frac{\stackrel{3a^2}{\cancel{6 a^3}}}{7 b} \cdot \frac{1}{\stackrel{\cancel{4 a}}{2}} \\ & =\frac{3 a^2}{14 b} ; a, b \neq 0\end{aligned}$$