Exam 3: Functions and Graphs

Graph the function. - $f(x)=(x-6)^{2}$

Give the equation of the horizontal asymptote of the rational function. - $h(x)=\frac{21 x^{2}}{7 x^{2}-2}$

Solve the problem. -At a manufacturing plant, the total cost (in dollars) to produce $x$ items is $C(x)=0.26 x+3350$ . What is the marginal cost per item?

Solve the problem. -At a manufacturing plant, the total cost (in dollars) to produce $x$ items is $C(x)=4.92 x+35,000$ What is the average cost per item?

Graph the function. - $f(x)=\sqrt[3]{x-2}$

Find the rule of a quadratic function whose graph has the given vertex and passes through the given point. -vertex $(-1,-6)$ ; point $(4,4)$

Graph the parabola. - $y=2(x-5)^{2}+1$

Determine whether the following rule defines $y$ as a function of $x$ . -The $x$ , y pairs: $\{(2,-7),(2,9),(4,-6),(8,-8),(12,3)\}$

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

Determine the vertex of the parabola. - $y=3 x^{2}-30 x+72$

Write the word or phrase that best completes each statement or answers the question. -The table shows the number of new AIDS cases (in thousands) in the U.S. in five consecutive years. Let $\mathrm{x}=1$ correspond to 1988 and let $\mathrm{f}(\mathrm{x})$ be the number of new AIDS cases (in thousands) in the U.S. in year $x$ . Using the points $(1,30.7)$ and $(5,46.0)$ , the following linear function is obtained to model the data: $f(x)=3.825 x+26.875$ . What does the slope, 3.825 , indicate?

Give the equation of the vertical asymptote(s) of the rational function. - $f(x)=\frac{8 x+1}{3 x-6}$

Graph the function. - $y=|x-3|-8$

Solve the problem. -An open-top box is to be made by cutting small identical squares from each corner of a 10-by - 10 -in. sheet of tin and bending up the sides. If each corner square is $x$ inches on a side, the volume of the box (in in. ${ }^{3}$ ) is given by: Find $\mathrm{V}(2)$ . $V(x)=100 x-40 x^{2}+4 x^{3}$

Solve the problem. -A new car was purchased for $\$ 14,500$ , and 3 years later it was worth $\$ 9100$ . Assume that the depreciation in value is given by a linear equation. Find the equation.

Use the vertical line test to determine if the graph is a graph of a function. -

Solve the problem. -Suppose the supply and demand for a certain videotape are given by: $\text { supply: } \mathrm{p}=\frac{1}{3} \mathrm{q}^{2} ; \quad \text { demand: } \mathrm{p}=-\frac{1}{3} \mathrm{q}^{2}+30$ Where $\mathrm{p}$ is price and $q$ is quantity. Find the equilibrium supply.

Evaluate the function. -Given that $f(x)=\sqrt{8-x}$ , find $f(1.4)$ .

Solve the problem. -Suppose that the population of a certain city during a certain time period can be approximated by: $P(x)=-0.1 x^{5}+3.2 x^{4}+4000$ Where $x$ is time in years since 1960. By sketching a graph of $\mathrm{P}(\mathrm{x})$ , estimate during what time period the population of the city was increasing.

Write the word or phrase that best completes each statement or answers the question -Suppose that during a flu epidemic in a particular city, the number of people, $N(x)$ , infected (in thousands) at the end of $x$ weeks is approximated by $N(x)=\frac{104 x}{x+21}$ What is the horizontal asymptote of the graph of this function? What does this suggest about the maximum number of people who will eventually be infected? Explain your reasoning.