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4.1: Function Definition
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A function is a rule that assigns to each element in the set of input values (the domain), one and only one element in the set of output values (the range).
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4.2: Function Notation
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Functions are written as ”f(x)= an algebraic expression”. Since y=f(x), f(x) is the same thing as y. This notation expresses x as the input into the function, and f(x) as the output from the function.
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4.3: Evaluating a Function
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When a function is evaluated, replace x with a given numeric value or an algebraic expression, and then simplify the result.
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4.4: Linear Functions
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A Linear Function is a function that has the form f(x)=mx+b . Any line that can be expressed in the form y=mx+b is also a function.
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4.5: Absolute-Value Functions
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To graph absolute-value functions, choose small values of x , and compute the value of f(x) from the given function to create ordered pairs. Three ordered pairs is the minimum amount needed to graph an absolute value function.
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4.6: Polynomial Functions
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A Polynomial Function is a function that can be written in the general form.
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4.7: Domain and Range of a Function
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The domain of a function is all possible values of x that can be used as input to the function, which will result in a real number as the output. The range of a function is the set of all possible output values of a function.
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4.8: Graphing Functions (without using Calculus)
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There are some basic functions, called toolkit functions, that students should recognize by their function definition and their graph. For each of these functions, x is the input variable, and f(x) is the output variable.
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4.9: Function Composition
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The notation f(g(x)) and g(f(x)) may be easier to understand than using the composition operator. For f(g(x)), think of wrapping a package. The gift is put into the box (the gift is g(x), the box is f(x)) and the wrapped present, f(x), contains the gift g(x).
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4.10: Finding all Real Roots of a Function
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To find the real roots of a function, find where the function intersects the x-axis. To find where the function intersects the x-axis, set f(x)=0 and solve the equation for x.
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4.11: Piecewise-Definition Functions
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Piecewise-Defined Functions are functions that are defined using different equations for different parts of the domain.
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4.12: Applied Examples of Functions
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Applied examples of function (AKA word problems!) can take many forms.