Exam 3: Functions and Graphs

Write a cost function for the problem. Assume that the relationship is linear. -A cable TV company charges $\$ 27$ for the basic service plus $\$ 8$ for each movie channel. Let $C(x)$ be the total cost in dollars of subscribing to cable TV, using $x$ movie channels.

Solve the problem. -If the average cost per unit $C(x)$ to produce $x$ units of plywood is given by $C(x)=\frac{1200}{x+40}$ , what is the unit cost for 10 units? Round your answer to the nearest cent.

Graph the function. - $y=3|x|-7$

Find the $x$ and $y$ intercepts. If no $x$ intercepts exist, state so. - $f(x)=2 x^{2}+8 x+5$

Write a cost function for the problem. Assume that the relationship is linear. -An electrician charges a fee of $\$ 55$ plus $\$ 40$ per hour. Let $C(x)$ be the cost in dollars of using the electrician for $x$ hours.

Solve the problem. -The number of mosquitoes $M(x)$ , in millions, in a certain area depends on the June rainfall $x$ , in inches: $\mathrm{M}(\mathrm{x})=4 \mathrm{x}-\mathrm{x}^{2}$ . What rainfall produces the maximum number of mosquitoes?

Solve the problem. -Suppose the supply and demand for a certain videotape are given by: $\text { supply: } \mathrm{p}=\frac{1}{3} \mathrm{q}^{2} ; \quad \text { demand: } \mathrm{p}=-\frac{1}{3} \mathrm{q}^{2}+44$ Where $p$ is price and $q$ is quantity. Find the equilibrium price.

Find the $x$ and $y$ intercepts. If no $x$ intercepts exist, state so. - $f(x)=2 x^{2}+10 x+5$

Graph the linear function. - $g(x)=x-4$

Evaluate the function. -Given that $f(x)=\sqrt{8-x}$ , find $f(m+2)$ .

Graph the rational function. - $f(x)=\frac{-1}{-5-4 x}$

Write the word or phrase that best completes each statement or answers the question -Suppose that a cost-benefit model is given by $f(x)=\frac{3.2 x}{100-x}$ where $f(x)$ is the cost in thousands of dollars of removing $x$ percent of a given pollutant. What is the vertical asymptote of the graph of this function? What does this suggest about the possibility of removing all of the pollutant? Explain your reasoning.

Graph the parabola. - $f(x)=(x+2)^{2}$

Graph the function. - $y=|-4-x|$

Write the word or phrase that best completes each statement or answers the question. -The chart below shows the profit-volume graphs of a single-product company for 1995 and 1996. Assume that unit sales prices were identical in both years. How did the fixed costs and unit variable costs in 1996 compare with those in 1995 ?

Find the $x$ and $y$ intercepts. If no $x$ intercepts exist, state so. - $f(x)=x^{2}+6 x+20$

Determine whether the following rule defines $y$ as a function of $x$ . -The $x$ , y pairs: $\{(-1,1),(2,8),(4,2),(9,-8),(11,-3)\}$

Solve the problem. -In one city, the temperature in Fahrenheit on a typical summer day can be approximated by the following function: $f(x)= \begin{cases}56+3.6 t & \text { if } 0 \leq t \leq 7 \\ 81.2 & \text { if } 7<t \leq 10 \\ -5.4 t+135.2 & \text { if } 10<t \leq 16\end{cases}$ Here, $t$ represents the number of hours since 6 a.m. Find the temperature at 5 p.m.

Graph the polynomial function. - $P(x)=-2 x(x+2)(x+1)$

Determine whether the following rule defines $y$ as a function of $x$ . - $x=y^{2}$