MTH 151
Quiz 1
Fall 2011
Show all work in a neat and organized fashion.
Clearly indicate your answers.
20 points possible.
1. (5 pts.) On the attached page, the graph of a function f is given.
(a) For what values of x is f(x)=2?
(b) State the domain and range of f.
(c) On what interval is f increasing?
2. (5 pts.) A weight attached to a vertical spring is bouncing up and down. Its distance from the floor
is given by a transformed sine or cosine graph. A stopwatch is started at time t=0 when the weight is at its high point,
70 cm above the floor.
At a time 2.4 seconds later, the weight reaches its next low point, 30 cm above the floor. Find a function that models
the distance from the floor to the weight as a function of time.
3. (5 pts.) Given F(x)=sin5(x3), find functions f, g, and h such that F=f°g°h.
4. (5 pts.) A tank holds 500 gallons of water, which drains from the bottom of the tank in
half an hour. The values in the table show the volume V(t) of water remaining in the tank
(in gallons) after t minutes.
t (min)
5
10
15
20
25
30
V(t) (gal)
347
222
125
56
14
0
(a) Find the average rate at which the volume V changed from t=5 to t=25. Include the units in your answer.
(b) Use the data in the table (without graphing) to estimate the rate at which the volume was changing
at t=8. Include the units in your answer.