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Page 2.1: Rational Expressions
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The quotient of two polynomial expressions is called a rational expression. We can apply the properties of fractions to rational expressions, such as simplifying the expressions by canceling common factors from the numerator and the denominator. To do this, we first need to factor both the numerator and denominator.
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Page 2.2: Avoiding Common Pitfalls
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Page 2.3: Solving Inequalities
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Page 2.4: Introduction to Functions
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Page 2.5: Graphing Types of Functions
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When both the input (independent variable) and the output (dependent variable) are real numbers, a function can be represented by a coordinate graph. The input is plotted on the x-axis and the output is plotted on the y-axis.
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Page 2.6: Finding Information About Functions From Graphs
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Page 2.7: Piecewise Defined Functions
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We begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define general algebraic functions and distinguish them from the transcendental functions we examine later in this chapter. We finish the section with piecewise-defined functions and take a look at how to sketch the graph of a function that has been shifted, stretched, or reflected from its initial form.