Math 1A – Chapter 1 Test – Sampling of Fair Game
Write all responses on separate paper.   Show your work for credit.

 

1.      Consider the line segment connecting the points  and .   

a.       Show that the slope of this line segment is given by the function .

b.      What is the domain of  m(x) ?

c.       What are the vertical asymptotes of  m(x) ?

d.      What is the horizontal asymptote of  m(x) ?

e.       What are the x-intercepts of m(x) ?

2.      Consider the function

a.       Find a formula  for the inverse function for f.

b.      Complete a short table of values (at least 3 coordinate pairs) and sketch a graph for both  and  showing the asymptotic behavior of each and their symmetry through the line y = x. 

3.      Consider the function .

a.       Write a formula for the function that results from stretching  vertically by a factor 5 and compressing horizontally by a factor .

b.      Write a formula for the function that results from stretching and compressing  as in part (a) and then shifting two units up and ¼ unit to the right?

4.      An initial population of 12,345 grows by 7% every month.

a.       Find a formula for the population size after n months, as a function of n.

b.      Find the average rate of change of the population over the twelfth week.

5.      Consider the function .

a.       Write the formula in complete square form; that is, find values for a, h, and k so that .

b.      Describe a sequence of transformations (horizontal/vertical shifts and/or horizontal/vertical stretches and/or reflections) to transform  to .

6.      Eliminate the parameter for the parametric equations:
                              
and sketch a graph for the curve over the interval .   Indicate with arrows the direction the curve follows over this interval.

7.      Write an equation for the cubic polynomial whose graph is shown

8.      Write parametric equations which describe the ellipse with Cartesian equation  and give a range of the parameter which completes one trace of the ellipse.

9.      Graph two different members of the family of functions described by  for two different positives values of c.   Write a sentence or two describing how the value c shapes the graph.

10.  Consider the function  

a.       Tabulate at least 3 different input/output values for .

b.      Tabulate at least 3 different input/output values for .