Question

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 (-∞, ∞)

Answer 1

Answer: Choice A

Note: the range should be $[-5, \infty)$. 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 $(-\infty, \infty)$ 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 $y \ge -5$ and that translates to the interval notation $[-5, \infty)$.

The square bracket says "include this endpoint" while the curved parenthesis says to exclude the endpoint. Your teacher mistakenly wrote $(-5, \infty)$ for choice A, when they should have written $[-5, \infty)$

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

Answer 2

Option A is the correct choice .

Domain will be → all real numbers .

Range will be → y belongs to R : y greater than or equal to -5 .

→ (x+3)^2 It means 0 to infinity

So (x+3)^2-5= (-5, infinity)

→ Range = (-5, infinity )