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. In the case of y=√(7-2x), we need to ensure that for every x in the domain, there is a unique y.
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Domain and Range
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. The range is the set of all possible output values (y-values) that result from the domain. For y=√(7-2x), we must identify the x-values that keep the expression under the square root non-negative.
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Square Root Function
The square root function, denoted as √x, is defined only for non-negative values of x, meaning that the expression inside the square root must be greater than or equal to zero. This restriction affects the domain of the function. In the equation y=√(7-2x), we set 7-2x ≥ 0 to find the valid x-values that form the domain.
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