What are the domain and range of this function y=(x+3)^2 -5 a. domain: (-∞, ∞) range: (-5, ∞)
b. domain: (-∞, ∞) range: (-∞, ∞)
c. domain: (-5, ∞) range: (-5, ∞)
d. domain: (-5, ∞) range (-∞, ∞)

Choice A

Note: the range should be . See explanation below.

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We can plug in any real number for x to get some output for y. The domain is the set of all real numbers in which we say which is interval notation. It represents the interval from negative infinity to positive infinity.

The range is the set of possible outputs. The smallest output possible is y = -5 which occurs at the vertex (3,-5). We can get this y value or larger. So we can describe the range as the set of y values such that and that translates to the interval notation .

The square bracket says "include this endpoint" while the curved parenthesis says to exclude the endpoint. Your teacher mistakenly wrote for choice A, when they should have written

I think either your teacher made a typo or somehow the formatting messed up. Either way, choice A is the closest to the answer.

no, because the sides are not congruent