Here are the essential concepts you must grasp in order to answer the question correctly.
Function Definition
A function is a relation where each input (x-value) corresponds to exactly one output (y-value). To determine if a relation defines y as a function of x, we check if any x-value is paired with more than one y-value. For example, the relation y = √(4x + 1) is a function because for each x, there is only one corresponding y.
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Domain
The domain of a function is the set of all possible input values (x-values) that can be used without causing any mathematical issues, such as division by zero or taking the square root of a negative number. For the function y = √(4x + 1), the domain is determined by the condition 4x + 1 ≥ 0, leading to x ≥ -1/4.
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Range
The range of a function is the set of all possible output values (y-values) that result from the domain. For the function y = √(4x + 1), since the square root function only produces non-negative outputs, the range is y ≥ 0. This means that as x varies within the domain, y will always be zero or greater.
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