Question

find the domain and range of function y=√(21-4x-x^2)
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Answer 1

Step-by-step explanation:

y=21−−√−4x−x2

This is a quadratic function with a non-rational constant term.

The domain is all allowable inputs. Since there is no division-by-zero or square-root-of-a-negative issue, this function is a polynomial function. All polynomial functions have “all reals” as their domain.

If you graph this function, you will see that the maximum output value is at the vertex, with the parabola opening downward, so the range is all y-values from the vertex downward. Complete the square to find the coordinates of the vertex, (h, k). The range will be the interval (-infinity, k).