Question

What is the domain of this function?

A. (-∞, 4)

B. (0, 4]

C. (-∞, 2]

D. (0, 2]

Answer 1

C.
`(-\infty\text{, }2]`

Explanation:

An arrow on a function means "goes to infinity". Of course, that infinite is in the direction the arrow is pointed at.
Here, we can see that the arrow points to the left. That means it goes to infinity in the left direction. Since all of the x values to the left of the y axis are negative, the function goes to minus infinity, but is not equal to it.

In addition, we can see that the function "stops" at the point (2, 4). Since the point's circle is not hollow, that point is included in the domain. Now, since we're asking for the domain, we'll be looking to take the x value of that point, which is x = 2.

Therefore, the domain is
`(-\infty\text{, }2]`