Exam 1: Functions and Graphs

What are the upper and lower bounds for the function f(x)=cos x-1 ?

Describe how the graph of $y=(5 x-5)^{2}$ can be obtained from the graph of $y=x^{2} .$

Give an example of a discontinuous function and state why it is discontinuous.

Find the domain of the function $f(x)=x^{2}+\sqrt{x-5}$ Give your answer in interval notation.

Five of the twelve basic functions are odd functions. Which are they?

What are the upper and lower bounds for the function $f(x)=\sin x+2 ?$

Solve $100 x^{2}+13 x=828$ by using the quadratic formula. Give your answer to one decimal place.

Juan drives in city traffic for 2 hours. He travels 62 miles during that time. He averages 26 miles per hour less on this drive than he does on a country highway. What is his average speed on the country highway?

A rectangular field is to be enclosed by a fence. An existing fence will form one side of the enclosure. The amount of new fence bought for the other three sides is 1200 feet. What is the maximum area of the enclosed field? formula. Give your answer to one decimal place.

Use a graphing calculator to determine all local maxima and/or minima for the function $y=2 x^{3}-7 x^{2}-4 x$ Give the values where the extremum occur to two decimal places.

Graph the relation defined by the parametric equations below. Use an appropriate window size for $-3 t 3$ . $x=5-2 t^{2}, y=2(t-1)$

A cylindrical tank with diameter $30 \mathrm{ft}$ is filled with gasoline to a depth of $60 \mathrm{ft}$ . The gasoline begins draining at a constant rate of 5 cubic feet per second. Write the volume of gasoline remaining in the tank $t$ seconds after the tank begins draining as a function of $t$ .

Let $f(x)=\sqrt{2-x}$ (a) Why does $f$ have an inverse that is a function? (b) Find a rule for $f^{-1}(x)$ and state its domain.

Find all vertical and horizontal asymptotes of the graph of $y=\frac{5 x}{2 x^{2}-11 x-6}$

Solve $\sqrt{x+2}=x-4$ algebraically and support graphically. Identify all extraneous solutions.

A cylindrical tank with diameter 25 meters is filled with gasoline to a depth of 40 meters. The gasoline begins draining at a constant rate of 4 cubic meters per second. Write the volume of gasoline remaining in the tank t seconds after the tank begins draining as a function of t .

Solve the equation $-x^{2}-3 x+10=0$ Give exact answers.

Write an equation that models the following and solve. How many gallons of vanilla ice cream with 12% butterfat must be mixed with 20 gallons of chocolate ice cream with 20% butterfat to make vanilla fudge ice cream with 15% butterfat?

Suppose the point (3, -5) lies on a graph of an even function. Determine a second point on the graph.

Let A represent the amount of money Paul has in his pocket. Paul and his girl friend go out to dinner. They spend x dollars on food, pay 8% tax on the dinner check, and leave a 15% tip (not including the tax). (a) Write a function relating the amount of money in Paul's pocket to the amount they spend on food for dinner. (b) If Paul has $46 in his pocket, what is the maximum amount they could spend on food for dinner?