This chapter deals with radicals and exponential functions--functions that
contain variable exponents. Here, the reader will review the meanings of
negative and fractional exponents, learn how to solve equations containing
radicals, and learn how to evaluate and graph exponential functions.
The first section reviews negative and fractional exponents. It explains how
to evaluate expressions containing negative and fractional exponents. This
material is also covered in Negative
Exponents and
Fractional Exponents.
The next section deals with equations containing radicals. Solving radical
equations is similar to solving ordinary equations using inverse operations, but
with two key differences--taking the inverse of a square leads to multiple
solutions, and taking the inverse of a square root can lead to false solutions.
This section explains how to find both solutions to an equation containing a
square, and how to recognize and eliminate the false solutions to an equation
containing a square root.
The final section introduces exponential functions. It
explains how to graph an exponential function and how to find the
domain and
range of an exponential function. It also
addresses translations,
stretches,
shrinks,
reflections, and
rotations of exponential functions.
Exponential functions are one of the many types of functions that mathematicians
study. They are useful because they describe many real-world situations,
including those in economics and in physics. In addition, they are interesting
from a mathematical perspective because they employ the variable in an unusual
way. While rational and polynomial functions multiply the variable by itself a
fixed number of times, exponential functions vary the number of times a
constant is multiplied by itself.
