Paul's Plumbing charges a flat fee of $\$ 50$ per service call plus an hourly rate of $\$ 42.50$. This means that cost is a function of the hours the job takes to complete plus the flat fee.

(a) Write this relationship in equation form;

(b) find the cost of a service call that takes $2 \frac{1}{2} \mathrm{hr}$;

(c) determine the number of hours the job took if the charge came to $\$ 262.50$;

(d) determine the domain and range of the function in this context, if your insurance company has agreed to pay for all charges over $\$ 500$ for the service call.

The volume of a cube depends on the length of the sides. In other words, volume is a function of the sides: $V(s)=s^3$.

(a) In practical terms, what is the domain of this function?

(b) Evaluate $V(6.25)$

(c) evaluate the function for $s=2 x^2$.

The general form of a linear equation is $ax+b y=c$, where $a$ and $b$ are not simultaneously zero.

(a) Find the $x$ - and $y$-intercepts using the general form (substitute 0 for $x$, then 0 for $y$ ). Based on what you see, when does the intercept method work most efficiently?

(b) Find the slope and $y$-intercept using the general form (solve for $y$ ). Based on what you see, when does the slope-intercept method work most efficiently?

Jackie has a gas-powered model boat with a $5$-oz gas tank. The boat will run for $2.5 \mathrm{~min}$ on each ounce. The number of minutes she can operate the boat is a function of how much gas is in the tank.

(a) Write this relationship in equation form

(b) find the domain and range of the function in this context.

John's old ' 87 LeBaron has a $15$ -gal gas tank and gets $23\ \mathrm{mpg}$. The number of miles he can drive is a function of how much gas is in the tank.

(a) Write this relationship in equation form

(b)find the domain and range of the function in this context.

In 1990, Americans bought an average of 143 meals per year at restaurants. This phenomenon continued to grow in popularity and in the year 2000, the average reached 170 meals per year.

(a) Find a linear function with $t=0$ corresponding to 1990 that models this growth

(b) discuss the slope ratio in context

(c) use the equation to estimate the average number of times an American will eat at a restaurant in 2010 if the trend continues.

Pick's theorem:$A=\frac{1}{2} B+I-1$

Pick's theorem is an interesting yet little known formula for computing the area of a polygon drawn in the Cartesian coordinate system. The formula can be applied as long as the vertices of the polygon are lattice points (both $x$ and $y$ are integers). If $B$ represents the number of lattice points lying directly on the boundary of the polygon (including the vertices), and $I$ represents the number of points in the interior, the area of the polygon is given by the formula shown. Use some graph paper to carefully draw a triangle with vertices at $(-3,1),(3,9)$, and $(7,6)$, then use Pick's theorem to find the triangle's area.

In 1990, the number of persons sentenced and serving time in state and federal institutions was approximately $740,000$. By the year 2000, this figure had grown to nearly $1,320,000$.

(a) Find a linear function with $t=0$ corresponding to 1990 that models this data.

(b) discuss the slope ratio in context.

(c) uses the equation to estimate the prison population in 2010 if this trend continues.

Celsius to Fahrenheit conversions: $C=\frac{5}{9}(F-32)$ The relationship between Fahrenheit degrees and degrees Celsius is modeled by the function shown.

(a) Find the Celsius temperature if ${ }^{\circ} \mathrm{F}=41$.

(b) Use the formula to solve for $F$ in terms of $C$, then substitute the result from part (a). What do you notice?

Retail sales of prescription drugs have been increasing steadily in recent years. In 1995, retail sales hit $\$ 72$ billion. By the year 2000, sales had grown to about $\$ 146$ billion.

(a) Use the relation (year, retail sales of prescription drugs) with $t=0$ corresponding to 1995 to find a linear equation modeling the growth of retail sales.

(b) Discuss what the slope indicates in this context.

(c) According to this model, in what year will sales reach $\$ 250$ billion?

(d) According to the model, what was the value of retail prescription drug sales in $2005 ?$

(e) How many years after 1995 will retail sales exceed $\$ 279$ billion?

(f) If yearly(sales totaled to ac $\$ 294$ billion, what year is it?

State the domain and range of each pointwise-defined relation.

Solve the following equations using a graphing calculator and the intersection-of-graphs method. For the first two exercises, carefully sketch the graphs you designate as $Y_1$ and $Y_2$ by hand before using your calculator.

$x-(3 x+1)=-0.5(4 x+6)+2$

Find whether the relations indicated represent functions or nonfunctions. If the relation is a nonfunction, explain how the definition of a function is violated.

$(-3,0),(1,4),(2,-5),(4,2),(-5,6),(3,6)$, $(0,-1),(4,-5)$, and $(6,1)$

The total value of the goods and services produced by a nation is called its gross domestic product or GDP. The $G D P$ per capita is the ratio of the GDP for a given year to the population that year and is one of many indicators of economic health. The GDP per capita (in $\$ 1000$ s) for the United States is shown in the table for selected years.

(a) Draw a scatterplot using scales that appropriately fit the data, then sketch an estimated line of best fit,

(b) decide if the association is positive or negative, then

(c) decide whether the correlation is weak or strong.

$$\begin{array}{|c|c|} \hline \begin{array}{c} x \\ (1970 \rightarrow 0) \end{array} & y \\ \hline 0 & 5.1 \\ \hline 5 & 7.6 \\ \hline 10 & 12.3 \\ \hline 15 & 17.7 \\ \hline 20 & 23.3 \\ \hline 25 & 27.7 \\ \hline 30 & 35.0 \\ \hline 33 & 37.8 \\ \hline \end{array}$$