Question

Function fis graphed below. What is the domain of the function f? у 4 3 2 1 4 -3 -2 2 3 -2 -3 -4 0-3

Answer 1

We assume in this answer a general case (since the question is not complete).

Suppose, we have the next function (a line):

As can we see from the graph, the values for x are all the values in the set of Real numbers. That is, the domain of the function is from -infinity to infinity.

The domain of a function is all the possible values for x in the represented function. That is all the values that this function can take.

On the other hand, the domain of the function:

`f(x)=\sqrt[]{6+x-x^2}`

It is restricted to values that comply with the next restriction (to be possible in the set of the Real numbers):

`6+x-x^2\ge0`

And solving for this, we have that the domain x must be greater or equal to -2 and less or equal to 3 or:

`-2\leq x\leq3`

The graphed function is sketched as follows: