Domain and Range of a Function

Definition: The domain of a function refers to the set of input values that return a real number from a function. The range is the set of the output values.

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Example: Find the domain and the range of y = √x + 4.

Solution:

Step 1: To determine the domain, check if there is any restriction on the possible x-values. Here we have √x and we know that taking the square root of a negative number does not return a real number thus x must be greater than or equal to zero. That is x ≥ 0. This may also be written as {x| x ≥ 0}.

Step 2: To determine the range, find the output values that correspond to the input values. Since x must be greater than or equal to 0, then y will always be greater than or equal to 4. So y ≥ 4 or {y| y≥ 4}.

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