Question

How do you find the Domain and Range of the following?02%7D%20%20-%204" id="TexFormula1" title="y = \sqrt{x + 2} - 4" alt="y = \sqrt{x + 2} - 4" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

Domain : x ≥ -2

Range : y ≥ -4

Step-by-step explanation:

The given function is:

y = √(x + 2)  - 4

Domain can be defined as the set of all possible values of x for which the function y is real and defined.

We can see that if we substitute x = -3 in the function, the value of under the underroot becomes negative, so the function becomes imaginary. If we substitute x = -2 or any value greater than that, the value of the function will be real and defined. Hence, the domain of the function is found x ≥ -2.

Range can be defined as all values of y which correspond to the domain. As minimum value of domain is x = -2, we substitute that in the function to get y = -4, which shows the minimum value of range. Hence, Range is y ≥ -4

We can see the domain and range in the graph