Question

Select the correct answer.

What are the domain and range of this function?
(x + 3)² - 5
A Domain: (0o,00)
Range (-00,00)
Domain: (-5,00)
Range: (-5,00)
C. Domain: (-0,00)
Range: (-5,00)
D. Domain: (-5,00)
Range: (-00,00)
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Answer 1

Explanation:

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

Doman: (-∞,∞). x∈R

Range:{-5,∞),y

the solution is C

Answer 2

Domain:
`(-\infty,\infty)`

Range:
`[-5,\infty)`

C

Explanation:

Please refer to the graph.

Recall that the domain is the span of x-values covered by the graph, while the range is the span of y-values covered by the graph.

So we have the equation.

`y=(x+3)^2-5`

This is a quadratic.

The domain of a quadratic is all real numbers. If you look at the graph, we can also see that the x-values will go on infinitely in both direction.

In interval notation, this is:

`(-\infty,\infty)`

For the range, note that the lowest the parabola goes is y=-5.

Therefore, our range is all values greater than or equal to -5.

In interval notation, this is:

`[-5,\infty)`

Note that we use brackets for the -5 because it is included in our range.

So, our answer is C