, for x=-2, -1, 0, 1.23, 1.414, 2.7. What happens when x < 0? Conclude that the natural domain of f is 
.
, for x=-4.37, -1.7, 0, 3.1415, 12.154, 16.2.
Are there any values of x for which g(x) is not defined as a real number? Explain.
, for t=-2.1, 0, 1.2, -4.1, 9. Most CAS define power functions only when the base is positive, which is not the case if t<0. In this case the natural domain of f is 
even though the CAS wants us to believe that it is 
. So, be careful when reading off results using a CAS.
. Evaluate g(-1), g(0), g(0.125), g(1), g(1.001), g(20), g(1000). Determine the behavior of g near x=1.
To do this use values of x just less than 1 and then values of x just larger than 1. 
Evaluate 
. Show that 
for every value of 
.
. a) Evaluate
. b) Explain your results.
c) What is the natural domain of f?
For example, to solve the inequality |2x-1| < 3 use your CAS to
a) Plot the graphs of y = |2x-1| and y=3 and superimpose them on one another
b) Find their points of intersection, and
c) Solve the inequality (see the figure below)
The answer is: -1 < x< 2.
b) |2x-2| < 4.2
c) |(1.2)x - 3| > 2.61
d) |1.3 - (2.5)x| = 0.5
e) |1.5 - (5.14)x| > 2.1
a)
b)
c)
Hint: Plot the functions on each side of the inequality separately, superimpose their graphs, estimate their points of intersection visually, and solve the inequality.
for small x's such as 
etc. Guess what happens to the values of f(x) as x gets closer and closer to zero.
, for 
. Use the Box method to evaluate the following terms, called the iterates of f: 
where each term is the image of the preceding term under f. Are these values approaching any specific value? This is an example of a chaotic sequence and is part of an area of mathematics called ``Chaos".
and compare these graphs with those of 
. Use this graphical information to guess the general shape of graphs of the form
for p > 1 and for 0 < p< 1. Guess what happens if p < 0?
for 
. a) Estimate the value of those points in the interval
where f(x) = 0.b) How many are there in each case?