Question

PLEASE HELP!!

Find the domain of the graphed function.

Answer 1

Answer: Choice A.
`x \le 0`

x can be any number smaller than 0, or it can be equal to 0 itself.

This is because the furthest to the right we can go is at x = 0. This endpoint is included due to the filled in circle at the endpoint.

There is no left boundary, so the graph goes on forever toward negative infinity.

We can say
`-\infty < x \le 0` but it's easier to say
`x \le 0`

The domain in interval notation would be
`(-\infty, 0]`. The square bracket says "include this endpoint". The curved parenthesis means "exclude this endpoint". We cannot reach either infinity, so we always use a curved parenthesis with either infinity.

As implied, the domain is the set of all possible x values of a function. The range is the set of all possible y values.

Answer 2

A

Explanation:

Recall that domain is simply the span of x-values a graph covers.

From the graph, we can see that the graph only covers x-values less than or equal to zero. Our x-values never cross and go beyond x = 0.

Therefore, our domain is all values less than or equal to 0.

As an inequality, this is:

`x\leq 0`

In conclusion, our answer is A.