Reference no: EM131005772
Question 1- For the function
a) Compute the average rate of change on the interval [-1, 2].
b) Find the end behavior of f (x).
c) Create a graph of f(x), and then draw the secant line whose slope you computed in part (a).
Question 2- A baseball player hits a ball. The motion of the ball can be described by the function
h(x) = (-116/30625)x2 + (232/175)x + 120,
which gives the height of the ball (in feet) as a function of x the ball's distance from the home plate (also in feet).
a) At what height did the player's bat make contact with the ball?
b) How far will the ball travel before it hits the ground?
c) What is the maximum height of the ball?
d) If an outfielder can catch a ball up to 11 feet in the air by jumping, at what distance should the outfielder stand to have a chance of catching the ball?
Question 3) a) Give an example of two quantities who are not likely represented by a function and explain why (make sure your explanation uses the definition of a function).
b) Give an example of two quantities who are likely represented by a function and explain why (again use the definition in you explanation).
c) What could the practical domain and range of your function from part (b) be? Justify you choice.
d) Is it likely that the function from part (b) has an inverse? Why or why not?
Question 4) An invertible function f (x) is defined in the table below, and the graph of a function g is also given.
| x |
f(x) |
| 0 |
-2 |
| 2 |
0 |
| 1 |
2 |
| -1 |
1 |
| 3 |
-1 |
a) Evaluate (f o f-1)(2).
b) Evaluate (g o f-1)( -1).
c) Evaluate (f-1 o f-1)(0).
d) Evaluate (f o g o f-1)(1).
e) Find a value of x satisfying 2 = (g o f)(x).
Question 5- Radium-226 is a naturally occurring radioactive material that can be found in many soils and rocks. Radium-226 decays into radon-222 which is a radioactive gas that can seep into basements through cracks in a buildings foundation. The National Academy of Sciences estimates that around 20,000 Americans die every year due lung cancer caused by radon gas making it the second leading cause of lung cancer behind smoking.
Suppose that the decay of a quantity of radon-222 is modeled by the function
q(t) = 500(0.8332620)t
that gives the quantity of radon-222 (in grams) as a function of time (in days). Interpret the values for the constants "a" and "b" in the context of this problem. After how many days will one third of the radon gas remain?
Question 6- Suppose that the number of subscribers to an internet service is inversely proportional to the pth power of the cost of the service. When the cost is $10 dollars there are 1,300,000 subscribers. When the cost is $15 there are 900,000 subscribers. Find a formula for the function s(c) that gives the number subscribers (in millions) as a function of the cost c in dollars.