It isn't always possible to determine. For example, it is unknown whether the Euler-Mascheroni constant (0.5772156649...) is rational or irrational.Most famous numbers and constants are known to be rational or irrational. If it can be expressed as a fraction a/b where a and b are integers, it's rational.
If it can't be expressed as a fraction then it is an irrational number
Discuss how you can use the zeros of the numerator and the zeros of the denominator of a rational function to determine whether the graph lies below or above the x-axis in a specified interval?
Statement 1 is true but totally unnecessary. As integer is always a rational and you do not need to convert it to a fraction to determine whether or not it is rational. A negative fraction is can be rational or irrational. The fact that it is negative is irrelevant to its rationality. An integer number over a zero denominator is not defined and so cannot be rational or irrational or anything. It just isn't.
Integers are rational numbers, whether they are positive or negative.
When the rational number is expressed as a ratio in its simplest form, if the only factors of the denominator are 2 and 5, then the number has a terminating representation. Otherwise it has an infinitely recurring sequence.
"Rational" is an adjective and so there cannot be "a rational" (and certainly not "an rational"). Any answer would depend on whether the question was about a rational number, a rational person, a rational argument or "a rational" combined with some other noun.
The decimal shows a repeating pattern. Repeating decimals are rational.
Any integer, whether positive or negative, is a rational number.
A negative sign, by itself cannot affect whether or not a number is rational.