[Note: This was Exam 1 given
September 19, 1995, in Math 106.]
Instructions: Show all of your work and clearly
explain your answers.
This is particularly important on problems
with a numerical answer, to allow the possibility
of partial credit. No books are allowed
during the exam, but you may use your calculator.
Problem [1] (8 pts) Suppose the Big Muddy Water Co. charges its customers
$10.00 a month plus $2.00 per 100 gallons of monthly water usage.
(a) Write down a formula for the monthly cost
of water service, as a function of the number of gallons of water used.
(b) What is the domain of this cost function?
(c) What is the range of this cost function?
Problem [2] (9 pts) The table gives some values for two functions, f(x) and g(x),
one of which is linear, the other exponential.
(a) Indicate which function is linear;
explain how you decided.
x f(x) g(x)
0.2 2.6 2.6
0.4 4.2 3.9
0.6 5.8 5.8
(b) Find the values f(0) and g(0) of each function
at 0; explain how you get your answers.
Problem [3] (8 pts) The graph of y = x2 is shifted up
one unit, then right 2 units,
then reflected across the x-axis, to give the graph of y = f(x).
(a) Sketch the graph of y = x2.
(b) Sketch the graph of y = f(x).
(c) Fill in the blanks: f(x) = _____(x + _____)2 + _____
Problem [4] (7 pts) Suppose you take a 5 hour trip by car, stopping once,
to eat lunch. Let d = f(t) be the distance covered
during the trip as a function of time t, where t is the number of hours
since the trip started.
(a) Draw a possible graph for f(t).
(b) Indicate whether f(t) is invertible and explain why or why not.
Problem [5] (7 pts) Bank A offers a savings account with an 8.3% annual interest
rate, compounded daily. Bank B offers a savings account with an 8.4% annual interest
rate, compounded twice a year, and Bank C offers a savings account with an 8.5% annual interest
rate, compounded continuously. Which bank offers the best deal and which offers
the worst deal? Explain how you decided.
Problem [6] (11 pts) A sinusoidal function y = f(x)
and a polynomial y = g(x) are graphed below.