Question

What is the domain of the function shown in the graph?​

Answer 1

Answer:

(-∞, ∞)

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

An asymptote is a line that the curve gets infinitely close to, but never touches.

The arrows on either end of a graphed curve show that the function continues indefinitely.  Therefore, we cannot assume there is an asymptote at x = -3 as we cannot see what happens to the curve as x approaches -∞.

Therefore, the domain of the given function is unrestricted:

• Solution:  { x | -∞ < x < ∞ }
• Interval notation:  (-∞, ∞)

Answer 2

Answer:

D: (-3,∞).

Step-by-step explanation:

Keep in mind that the domain of a function that we see in a graph is basically just from what x point to what x point the function moves. In other words, the domain is to say what is the horizontal extension that the function occupies on the cartesian plane.

In this case, as you may see, the fuction seems to go all the way to infinite +x, becaue the arrow goes to the right and it doesn't seem to stop after the graph cuts. Now, the other end of this interval appears to be x= -3. because the line of the fuction gets close to that x value but never touches it, probably because the function has an asymptote on the value x= -3.

Therefore, on mathematical notation, the intervar of the domain of this function should be expressed like this:

D: (-3,∞).

Note that we use parenthesis next to the -3, because we assumed that the function never touches the value, because it doesn't have it as domain, but it goes close to it. Also, we used parenthesis next to the infinity symbol because infinity is always notated like that, always goes with parenthesis.

In case you have a function that does include the values that you type in the interval, you would type a "{" or "}" next to the number. Example:

D: {4, 5}