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5: Polynomial and Rational Functions

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  • Page ID
    106513

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    • 5.0: Prelude to Polynomial and Rational Functions
      Digital photography has dramatically changed the nature of photography. No longer is an image etched in the emulsion on a roll of film. Instead, nearly every aspect of recording and manipulating images is now governed by mathematics. An image becomes a series of numbers, representing the characteristics of light striking an image sensor. When we open an image file, software on a camera or computer interprets the numbers and converts them to a visual image.
    • 5.1: Quadratic Functions
      In this section, we will investigate quadratic functions, which frequently model problems involving area and projectile motion. Working with quadratic functions can be less complex than working with higher degree functions, so they provide a good opportunity for a detailed study of function behavior.
    • 5.2: Quadratic inequalities
    • 5.3: Applications with quadratic functions
    • 5.4: Power Functions and Polynomial Functions
      Suppose a certain species of bird thrives on a small island. The population can be estimated using a polynomial function. We can use this model to estimate the maximum bird population and when it will occur. We can also use this model to predict when the bird population will disappear from the island. In this section, we will examine functions that we can use to estimate and predict these types of changes.
    • 5.5: Dividing Polynomials
      We are familiar with the long division algorithm for ordinary arithmetic. We begin by dividing into the digits of the dividend that have the greatest place value. We divide, multiply, subtract, include the digit in the next place value position,. Division of polynomials that contain more than one term has similarities to long division of whole numbers. We can write a polynomial dividend as the product of the divisor and the quotient added to the remainder.
    • 5.6: Inverses and Radical Functions
      In this section, we will explore the inverses of polynomial and rational functions and in particular the radical functions we encounter in the process.

    Thumbnail: Identifying the behavior of the graph at an x-intercept by examining the multiplicity of the zero.

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