Here are the essential concepts you must grasp in order to answer the question correctly.
Domain of a Function
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. For rational functions, the domain is typically restricted by values that make the denominator zero, as division by zero is undefined.
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Finding Roots of a Quadratic Equation
To determine the values that restrict the domain, one must find the roots of the quadratic equation in the denominator. This involves using methods such as factoring, completing the square, or applying the quadratic formula to identify the x-values that make the denominator zero.
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Inequalities and Exclusions
Once the roots of the denominator are found, these values must be excluded from the domain. The domain can then be expressed in interval notation, indicating all real numbers except for the points where the function is undefined due to division by zero.
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