Chapter 3: Polynomial and Rational Functions
...............................................................
155
...............................................
155
Section 3.1 Exercises
...................................................................................................
162
Section 3.2 Quadratic Functions
..................................................................................
163
Section 3.2 Exercises
...................................................................................................
173
Section 3.3 Graphs of Polynomial Functions
..............................................................
178
Section 3.3 Exercises
...................................................................................................
187
Section 3.4 Rational Functions
....................................................................................
191
Section 3.4 Exercises
...................................................................................................
204
Section 3.5 Inverses and Radical Functions
................................................................
210
Section 3.5 Exercises
...................................................................................................
216
A square is cut out of cardboard, with each side having some length
L
.
If we wanted to
write a function for the area of the square, with
L
as the input, and the area as output, you
may recall that area can be found by multiplying the length times the width.
Since our
2
)
(
L
L
L
L
A
=
⋅
=
Likewise, if we wanted a function for the volume of a cube with each side having some
length
L
, you may recall that volume can be found by multiplying length by width by
height, which are all equal for a cube, giving the formula:
3
)
(
L
L
L
L
L
V
=
⋅
⋅
=
These two functions are examples of
power functions
; functions that are some power of
the variable.
Power Function
A
power function
is a function that can be represented in the form
p
x
x
f
=
)
(
Where the base is the variable and the exponent,
p
, is a number.
Example 1
Which of our toolkit functions are power functions?
The constant and identity functions are power functions, since they can be written as
0
)
(
x
x
f
=
and
1
)
(
x
x
f
=
respectively.
The quadratic and cubic functions are both power functions with whole number
powers:
2
)
(
x
x
f
=
and
3
)
(
x
x
f
=
.
This chapter is part of
Precalculus: An Investigation of Functions
© Lippman & Rasmussen 2011.
This material is licensed under a Creative Commons CCBYSA license.
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 Spring '11
 Curtis
 pH, Quadratics, Quadratic equation, ........., Elementary algebra, Degree of a polynomial

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