We have the expression:
When we have rational functions, where the denominator is a function of x, we have a restriction for the domain for any value of x that makes the denominator equal to 0.
That is because if the denominator is 0, then we have a function f(x) that is a division by zero and is undefined.
If we have a value that makes f(x) to be undefined, then this value of x does not belong to the domain of f(x).
Expression:
Answer: There is no restriction for x in the expression.
Answer:
(-3,6)
It is -3 on the x line and 6 on the y.
Hope this helps!
I assume you mean one that is not rational, such as √2. In such a case, you make a reasonable estimate of it's position, and then label the point that you plot.
For example, you know that √2 is greater than 1 and less than 2, so put the point at about 1½ (actual value is about 1.4142).
For √3, you know the answer is still less than 4, but greater than √2. If both of those points are required to be plotted just make sure you put it in proper relation, otherwise about 1¾ is plenty good (actual value is about 1.7321).
If you are going to get into larger numbers, it's not a bad idea to just learn a few roots. Certainly 2, 3, and 5 (2.2361) and 10 (3.1623) shouldn't be too hard.
Then for a number like 20, which you can quickly workout is √4•√5 or 2√5, you could easily guess about 4½ (4.4721).
They're usually not really interested in your graphing skills on this sort of exercise. They just want you to demonstrate that you have a grasp of the magnitude of irrational numbers.
