Math 10—College Algebra—Chapter 2 Test—Fall ’04       Name_______________________

Show your work for credit.  Write all responses on separate paper.

 

1.      Consider the following equations relating x and y :

a.   

b. 

c.   

               i.      For each, sketch a graph.  Remember to scale and label axes.  You may use a graphing utility to help with (c). 

       ii.            If the equation represents y as a function of x write “y is a function of x” by its graph, or, if the equation represents x as a function of y write “x is a function of y” by its graph.

2.      Let  and 

a.       What is the domain of  f  ? 

b.      What is the domain of  g ?

c.       Evaluate  

d.      What is the domain of  ?

3.      Suppose the rate, R, of population growth is jointly proportional to the present population size, p,  and the amount by which that size falls short of the carrying capacity C – p.

a.       Assuming the constant of proportionality is k, write an equation relating R to p.  This equation will also involve the parameters C and k.

b.      Suppose the carrying capacity is C = 1000 and a polution of p = 800 yields a population growth rate R = 3%.  What is the value of k?  What will the growth rate be if p = 500?

4.      Find the average rate of change of the function   over the interval .

5.      Consider the function .

a.       Make a table of values and sketch a graph of this function.

b.      Use these results and the properties of function transformation to make a table for  and sketch its graph. 

6.      Consider

a.       Write the function in vertex form.

b.      Find exact coordinates for the intercepts and sketch a graph for the function showing the coordinates of the vertex and all intercepts.

7.      Find the inverse function for  and sketch a graph of f and its inverse together, showing the symmetry through the line y = x.  As always, scale and label axes.

8.      Recall that the volume of a cylinder with height h and radius r is .  Suppose the sum of the height of a circular cylinder with the radius of its base is 5 cm.  What is its maximum volume?