Question

please answer question with explanation

Answer 1

Answer:

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

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

Step-by-step 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 :)