Question

Please answer question with explanation

Answer 1

Domain:
`\{x|x\in\mathbb{R}\}`

Range:
`\{y|y\in\mathbb{R},y\leq -2\}`

Explanation:

The domain is the span of x-values the graph covers.

The range is the span of y-values the graph covers.

The given graph is a quadratic. We can see that the x-values will extend infinitely in both directions.

Thus, the domain is all real numbers.

In set notation, this is:

`\{x|x\in\mathbb{R}\}`

From the graph, we can see that the maximum value is y=-2. The graph won't ever go above this.

So, the range is all real numbers less than or equal to -2.

In interval notation, this is:

`\{y|y\in\mathbb{R},y\leq -2\}`

And we are done :)