domainand range- open text book store（domainand range - store open text读书）.doc

Chapter 3: Polynomial and Rational Functions Section 3.1 Power Functions Polynomial Functions 155 Section 3.2 Quadratic Functions 163 Section 3.3 Graphs of Polynomial Functions 176 Section 3.4 Rational Functions 188 Section 3.5 Inverses and Radical Functions 206 Section 3.1 Power Functions Polynomial Functions A square is cut out of cardboard, with each side having 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 the area of a rectangle can be found by multiplying the length times the width. Since our shape is a square, the length the width are the same, giving the formula: Likewise, if we wanted a function for the volume of a cube with each side having some length L, you may recall volume of a rectangular box can be found by multiplying length by width by height, which are all equal for a cube, giving the formula: 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 Where the base is a 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 and respectively. The quadratic and cubic functions are both power functions with whole number powers: and . The reciprocal and reciprocal squared functions are both power functions with negative whole number powers since they can be written as and . The square and cube root functions are both power functions with fractional powers since they can be written as or . Try it Now 1. What point(s) do the toolkit power functions have in common? Characteristics of Power Functions Shown to the right are the graphs of , all even whole number powers. Notice that all these graphs have a fairly similar shape, very similar to the quadratic toolkit, but as the pow