MAC 1140 – In Class Exercises – 1/22/2015
1.
Suppose a particle distance (in meters) is determined by the function s  t   t 4  2t 3  t 2  t for
t  0 (in seconds). The table below list some order pairs on the graph of this function.
a. Calculate the average rate of change over the first 3 seconds that the particle is moving.
b. Approximate the instantaneous rate of change when t  1 . The exact instantaneous
rate of change when t  1 is 1
2.
m
.
s
Graph the function and fill in the table.
 x  1 if x  0
f  x  
.
 x  1 if x  0
3.
Graph each function.
a.
f  x     x  2  4
3
b. g  x   
1
2
 x  3
2
4.
Let f  x   x 2  x  3 and g  x   2 x  1 . Determine:
a.
b.
c.
f
g
g
g  x 
f  x 
g  x 
d. Construct and simplify the difference quotient for f  x  .
5. If h  x    f
a.
b.
g  x  then determine f  x  and g  x  for each function.
h  x    x 2  3
3
3
1 x
2
6. Let f  x   2  x and g  x   2 x  1 and determine:
a.
b.
c.
 f  g  0 
 fg  0 
 f  g  0 
 f 
  2
g
d. 
7. Using the graph of f  x  below graph the following, labeling 4 points on each graph as in the
graph given.
a.
f  x 1
b.
2 f  x
c.
 f  x
d. Write a formula for f  x  . Hint: It will be a piecewise defined function.