* Indicates a problem that is more challenging or involved.

When creating graphs or charts, it is helpful to begin by creating a table of values representing the independent variable (e.g., x) values and dependent variable (e.g., y) values to be graphed.  When graphing sine functions, the convention adopted here is that independent variables labeled x refer to angles of rotation in radians (e.g., y = A · sin(B(x - D)) + C) and independent values labeled t refer to time in seconds (e.g., s(t) = A · sin(2 · · f · t + ) + c).

1. The preceding bar graph represents the average number of patients seen at a clinic over a six-month period.  Use this graph to answer the following questions.
   
   1. What is the average daily-difference between the number of hearing patients and the number of speech patients?
      

   2. What is the average number of speech patients seen daily?  What is the average number of hearing patients seen daily?  Is either of these averages a better indication of what actually happens on any particular day of the week?  Why?
      

   3. What are other simple ways of summarizing data besides an average?  Give examples of these ways based on the data in the chart. (Dig out your old statistics text if necessary!)
      

   
   

2. Graph the following functions (Careful hand-drawn sketches are fine).  Use Excel (or a graphing calculator) to check your work and to help you understand the form of the functions. See Excel Assignments Hints under Resources for help graphing functions.

   a.     f(x) = sin(2x)	b.     f(x) = sin(x + )	c.    f(x) = sin(0.25x)
   d.     f(x) = sin(x) + 2	e.     f(x) = 3sin(x)	f.     f(x) = sin(2x + /2)
   g.     f(x) = sin(2··x)

    

3. Solve the following equations for x.
   

   a.    x 2 + 3x  =  18	b.  Wx - 10x  =  2(10-x)	c.     1/x  =  440
   d.     2 x  =  1/16	e.     1/x  =  10000

 

4. Write the equation of a sine function that represents each of the following graphs.

   a.

   

   b.

   

   c.*

   

    

5. Write sine functions for the following pure tones (with amplitude 1, no phase shift, and no vertical shift).  Graph each function for one or two complete periods beginning with time t = 0 seconds (Choose appropriate scales for the x and y axes).   Also state the period in seconds of each sine function.

   a.     200 Hz

   b.     1000 Hz

   c.     16000 Hz