Each of the following data tables represents a function.

a. Identify the independent and dependent variables, and describe the domain and range.

b. Make a clear graph of the function. Explain how you decide on the shape of the curve used to fill in the gaps between the data points.

c. Describe the function in words.

Speed $(\mathrm{mi} / \mathrm{hr})$	Stopping Distance (reaction plus braking in $\mathrm{ft}$ )
$10$	$13$
$20$	$39$
$30$	$75$
$40$	$117$
$50$	$169$
$60$	$234$
$70$	$312$

Using the tables that define $f$ and $g$, determine whether each statement is true or false.

$$\begin{aligned} &\begin{array}{c|c} \hline x & f(x) \\ \hline-4 & -1 \\ \hline-3 & -2 \\ \hline-2 & -3 \\ \hline-1 & -4 \\ \hline \end{array} &\begin{array}{c|c} \hline \boldsymbol{x} & g(x) \\ \hline-1 & -4 \\ \hline-2 & -3 \\ \hline-3 & -2 \\ \hline-4 & -1 \\ \hline \end{array} \end{aligned}$$

$$f(-4)-f(-2)=2$$

Write a class that contains the following two methods:

//Convert from Mile to Kilometer 
  public static double mileToKilometer(double mile)
  
//Convert from Kilometer to Mile 
  public static double kilometerToMile(double kilometer)

The formula for the conversion is:

1mile=1.6 kilometers

Write a test program that invokes these methods to display the following tables:

Suppose that one day all 200+ million people in the United States climb up on tables. At time t = 0, they all jump off. The resulting shock wave starts the earth vibrating at its fundamental period, 54 minutes. The surface first moves down from its normal position and then moves up an equal distance above its normal position. Assume that the amplitude is 50 meters.

At what time will the surface be farthest above its normal position?

Stock Tables For International Business Machines (IBM):

a. What is the difference between the highest and lowest prices paid for this stock during the last 52 weeks?

b. Suppose that you own 750 shares of this stock. What dividend do you receive this year?

c. How many shares of this stock were sold during the trading day?

d. Did the price of a share of this stock increase or decrease during the day shown in the table?

e. What was the price of a share of this stock at the start of the trading day?

Estimate the degree of dissociation of a $0.200 \mathrm{~m}$ solution of nitrous acid $\left(K_a=4.00 \times 10^{-4}\right)$ that is also $0.500 \mathrm{~m}$ in the strong electrolyte given in parts (a) through ( c). Use the data tables to obtain $\gamma_{\pm}$, as the electrolyte concentration is too high to use the Debye-Hückel limiting law. a. $\mathrm{Ba}(\mathrm{Cl})_2$ b. $\mathrm{KOH}$ c. $\mathrm{AgNO}_3$ Compare your results with the degree of dissociation of the acid in the absence of other electrolytes.

Using the table below, complete the tables for g, h, k, m, where:

(a) $g(x)=f(x-1)$

(b) $h(x)=f(x+1)$

(c) $k(x)=f(x)+3$

(d) $m(x)=f(x-1)+3$

Explain how the graph of each function relates to the graph of f(x).

Using the tables that define $f$ and $g$, determine whether each statement is true or false.

$$\begin{aligned} &\begin{array}{c|c} \hline x & f(x) \\ \hline-4 & -1 \\ \hline-3 & -2 \\ \hline-2 & -3 \\ \hline-1 & -4 \\ \hline \end{array} &\begin{array}{c|c} \hline \boldsymbol{x} & g(x) \\ \hline-1 & -4 \\ \hline-2 & -3 \\ \hline-3 & -2 \\ \hline-4 & -1 \\ \hline \end{array} \end{aligned}$$

The range of $f=$ the domain of $g$.

The following tables show the percentage of smokers among the adult population in the United States for every five years since 1990. Find the least squares lines for these data, and use your answer to predict the percentage of that sex who will smoke in the year 2020 (x = 7).

$$\begin{array}{ccc} \hline & \boldsymbol{x} & \text { Percent Females } \\ 1990 & 1 & 23 \\ 1995 & 2 & 23 \\ 2000 & 3 & 21 \\ 2005 & 4 & 18 \\ 2010 & 5 & 18 \\ \hline \end{array}$$

(a) use a graphing utility to graph the two equations in the same viewing window and (b) use the table feature of the graphing utility to create a table of values for each equation. (c) What do the graphs and tables suggest? Verify your conclusion algebraically. $y_{1}=2\left[\ln 8-\ln \left(x^{2}+1\right)\right], \quad y_{2}=\ln \left[\frac{64}{\left(x^{2}+1\right)^{2}}\right]$

Use the tables to evaluate the following.

$${\begin{array}{|c|c|c|c|c|c|} \hline x&0&1&2&3&4\\ \hline f(x)&1&3&5&4&2\\ \hline \end{array}}$$

$${\begin{array}{|c|c|c|c|c|c|} \hline x&-1&1&2&3&4\\ \hline g(x)&0&2&1&4&5\\ \hline \end{array}}$$

• $g^{-1}(0)$

Use the tables to evaluate the following.

$${\begin{array}{|c|c|c|c|c|c|} \hline x&0&1&2&3&4\\ \hline f(x)&1&3&5&4&2\\ \hline \end{array}}$$

$${\begin{array}{|c|c|c|c|c|c|} \hline x&-1&1&2&3&4\\ \hline g(x)&0&2&1&4&5\\ \hline \end{array}}$$

• $\left(g \circ f^{-1}\right)(5)$

Complete the tables and use them to find each limit (or state that it does not exist). Round calculations to three decimal places.

a. $\lim _{x \rightarrow 2^{-}}(4 x+2)$

b. $\lim _{x \rightarrow 2^{+}}(4 x+2)$

c. $\lim _{x \rightarrow 2}(4 x+2)$

$$\begin{array}{ll} \hline x & 4 x+2 \\ 1.9 & \\ 1.99 & \\ 1.999 & \\ \hline \end{array}$$

$$\begin{array}{ll} \hline x & 4 x+2 \\ 2.1 & \\ 2.01 & \\ 2.001 & \\ \hline \end{array}$$

In 2000 B.C., the Babylonians solved polynomial equations using tables of values. One such table gave values of y³ + y². To be able to use this table, the Babylonians sometimes had to manipulate the equation, as shown below. ax³ + bx² = c, a³x³/b³ + a²x²/b² = a²c/b³, (ax/b)³ + (ax/b)² = a²c/b³ They then found a²c/b³ in the y³ + y² column of the table. Because the corresponding y-value was y = ax/b, they could conclude that x = by/a. How can you modify the method described above for equations of the form

$$ax^4 + bx^3 = c?$$