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Brilliant_brown [7]
3 years ago
14

What are the domain and range of this function y=(x+3)^2 -5

Mathematics
2 answers:
n200080 [17]3 years ago
8 0

Answer: Choice A

Note: the range should be [-5, \infty). See explanation below.

===================================================

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.

Tatiana [17]3 years ago
4 0

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 )

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You can answer this question by plugging the given values into point-slope form, which is y - y_{1} = m (x - x_{1}). M will represent slope and x_{1} and y_{1} will represent the x and y coordinates.

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   y + 5 = 4m - 16    Subtract 5 from both sides
       
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