Here are the essential concepts you must grasp in order to answer the question correctly.
Function Operations
Function operations involve combining two functions to create a new function. In this case, f-g means subtracting the function g(x) from f(x). Understanding how to perform these operations is essential for manipulating and analyzing functions in algebra.
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Multiplying & Dividing Functions
Domain of a Function
The domain of a function is the set of all possible input values (x-values) for which the function is defined. For rational functions, the domain is restricted by values that make the denominator zero. Identifying the domain is crucial for ensuring that the function behaves correctly and does not produce undefined values.
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Domain Restrictions of Composed Functions
Rational Functions
Rational functions are ratios of two polynomials. They can exhibit unique behaviors, such as asymptotes and discontinuities, particularly where the denominator equals zero. Understanding the properties of rational functions helps in analyzing their graphs and determining their domains.
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Intro to Rational Functions