Identify the asymptotes, domain, and range of the function.

$$f ( x ) = \frac { 3 } { x + 2 } + 1$$

Determine whether the following statements are true and give an explanation or counterexample. If p(x) is the Taylor series for f centered at 0, then p(x-1) is the Taylor series for f centered at 1.

Solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.

$$a = 63 , b = 22 , c = 50$$

What alcohols are obtained from the reduction of the following compounds with sodium borohydride? a. 2-methylpropanal, b. cyclohexanone, c. 4-tert-butylcyclohexanone, d. acetophenone

In December 2011, Consumer Reports published their study of labeling of seafood sold in New York, New Jersey, and Connecticut. They purchased 190 pieces of seafood from various kinds of food stores and restaurants in the three states and genetically compared the pieces to standard gene fragments that can identify the species. Laboratory results indicated that 22% of these packages of seafood were mislabeled, incompletely labeled, or misidentified by store or restaurant employees. a) Construct a 95% confidence interval for the proportion of all seafood packages in those three states that are mislabeled or misidentified. b) Explain what your confidence interval says about seafood sold in these three states. c) A 2009 report by the Government Accountability Board says that the Food and Drug Administration has spent very little time recently looking for seafood fraud. Suppose an official said, "That's only 190 packages out of the billions of pieces of seafood sold in a year. With the small number tested, I don't know that one would want to change one's buying habits." (An official was quoted similarly in a different but similar context). Is this argument valid? Explain.

Choose the best answer. The five-number summary for a data set is given by min = 5,

$$Q_1 = 18,$$

median = 20,

$$Q_3 = 40,$$

max = 75. If you wanted to construct a boxplot for the data set (that is, one that would show outliers, if any existed), what would be the maximum possible length of the right-side "whisker"? (a) 33 (b) 35 (c) 45 (d) 53 (e) 55

Use the Half-angle Formulas to find the exact value of each expression. $\tan \frac{9 \pi}{8}$

Let $T$ be a linear operator on $R^n$ and $\mathcal{B}$ be an ordered basis for $R^n$. Prove the following results: (a) For every vector $v$ in $R^n$, $[T(v)]_B=[T]_B[v]_B$. (b) If $C$ is an $n\times n$ matrix such that $[T(v)]_B=C[v]_B$ for every vector $v$ in $R^n$, then $C=[T]_B$.

Solve each trigonometric equation for values between 0 and

$$2 \pi$$

$$2 \cos ^ { 2 } \theta - 1 = 0$$

Find the center and radius of the circle and graph it.

$$( x + 4 ) ^ { 2 } + y ^ { 2 } = 1$$

Give the z -score for a measurement from a normal distribution for the following: 1 standard deviation above the mean

A function is given. Determine (a) the net change and (b) the average rate of change between the given values of the variable.

$$f ( x ) = 1 - 3 x ^ { 2 } ; \quad x = 2 , x = 2 + h$$

Determine the mass (in grams) of exactly 100 million atoms of fluorine if the relative atomic mass of fluorine is 18.998403 on a scale on which exactly 12 is the relative atomic mass of ^12C.

Nutritionists recommend that teenagers consume 1300 milligrams of calcium per day. Use dimensional analysis to convert this rate to grams per year.