Calculus I Exam I Sample Questions

The graph of y = f(x) is graphed below. Use it to answer the following questions:
- Solve the equation f(x) = -1.
- Find f(-1).
- Graph y = 0.5(f(x-1)) + 3.
- What are the domain and range of f?
- When is f increasing?
- When is f concave down?
- If g(x) = -x² + 4, find f(g(2)), g(f(3)), and (g+f)(2).
For the table given below:

x 1 ____ 3

y 4 ____ 8
- Complete the table so that the data would be linear.
- Complete the table so that the data would be exponential.
- Complete the table so that the data would be trigonometric.
- Complete the table so that the data would be logarithmic.
For each of the following graphs, label the type of function it is, and find a possible equation for it:
Solve the equation
x³ - 109x² -890x + 1000 = 2^x

and explain why you think you have all the solutions.
You have $500 invested in a bank account earning 8.2% compounded annually.
- Write an equation for the money M in your account after t years.
- How long will it take to triple your money? Do this algebraically and graphically.
- Suppose the interest were compounded monthly instead, that is, you earned 8.2/12 % interest each month. What interest would you then earn for 1 year?
Water is poured into the vase below at a constant rate, and the vase is filled up in exactly 10 seconds.
- Sketch a graph of the height of the water versus the time.
- At what time is the height increasing the most quickly?
- At what time is the height increasing the most slowly?
- Is there a time at which the height is accelerating the most quickly? If so, when, and how do you know?
Find the equation of the parabola below; use that then to find the missing coordinates of the given intersection points, and then finally the equation of the line.

x	1	____	3
y	4	____	8