Give an example of a Rational Function that is undefined at x=a where a is a Real Number. Next, state the domain of your Rational Function using both Set Notation and Interval Notation

1/(x-a)

the domain is all real numbers EXCLUDING x = a where the function is undefined.

Sure! One example of a Rational Function that is undefined at x=a, where a is a real number, is f(x) = (x^2 - 1)/(x - a). In this case, the function will be undefined when x = a because it would result in division by zero.

Now, let's determine the domain of this Rational Function using both Set Notation and Interval Notation.

Set Notation represents the domain as a set of numbers, while Interval Notation represents the domain as an interval on the number line.

To find the domain, we need to consider values of x for which the function is defined, i.e., where the denominator is not zero.

Set Notation:
The domain of the given rational function in set notation can be expressed as follows:
D = {x ∈ ℝ: x ≠ a}

Interval Notation:
Now let's convert the set notation to interval notation.
The domain of the rational function in interval notation can be written as:
(-∞, a) U (a, ∞)

In interval notation, (-∞, a) indicates all values less than a, but not including a, and (a, ∞) indicates all values greater than a, but not including a.

So, the domain of f(x) = (x^2 - 1)/(x - a) in both Set Notation and Interval Notation is D = {x ∈ ℝ: x ≠ a} = (-∞, a) U (a, ∞).