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# Chapter 3 - Chapter 3 Polynomial and Rational Functions...

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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 CC-BY-SA license.

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Chapter 3 - Chapter 3 Polynomial and Rational Functions...

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