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Q: Some rational functions have more than one vertical asymptote?

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That is not correct. A rational function may, or may not, have a vertical asymptote. (Also, better don't write questions with double negatives - some may find them confusing.)

Definition: If lim x->a^(+/-) f(x) = +/- Infinity, then we say x=a is a vertical asymptote. If lim x->+/- Infinity f(x) = a, then we say f(x) have a horizontal asymptote at a If l(x) is a linear function such that lim x->+/- Infinity f(x)-l(x) = 0, then we say l(x) is a slanted asymptote. As you might notice, there is no generic method of finding asymptotes. Rational functions are really nice, and the non-permissible values are likely vertical asymptotes. Horizontal asymptotes should be easiest to approach, simply take limit at +/- Infinity Vertical Asymptote just find non-permissible values, and take limits towards it to check Slanted, most likely is educated guesses. If you get f(x) = some infinite sum, there is no reason why we should be able to to find an asymptote of it with out simplify and comparison etc.

A rational expression is an expression that includes only additions, subtractions, multiplications and divisions. Some of the things that will make an expression irrational (not rational) are square roots, higher-level roots, non-integer powers, exponentials (powers in which the variable expression occurs in the exponent), and common functions such as logarithms or trigonometric functions.

There are some relationships but not all relationships are always true. Any function can be represented by an equation. But all equations are not functions. For example, y = sqrt(x) is the equation of the square root relationship which can be graphed as a parabola on its side, but it is not a function. It has slopes at each point. Some functions can be plotted as graphs but not all. A function such as f(x) = 1 when x is rational, and f(x) = 0 when x is irrational has no slope and cannot be plotted as a graph. A graph of a vertical line is not a function.

Such functions are defined as one polynomial divided by another polynomial. Their properties include that they are defined at all points, except when the denominator is zero. Also, such functions are continuous at all points where they are defined; and all their derivatives exist at any point where they are defined.For more details, I suggest you read the Wikipedia article - or some other source - on "Rational function".

Yes, but only in some cases and they are special types of integrals: Lebesgue integrals.

If you have some reasonable degree of understanding about how things happen in the real world and how the world functions, and if you have an adequate amount of information about the situation about which you wish to make a decision, you can then apply this knowledge in order to make a rational decision.

It is some an order based on some logical or rational basis.

"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.

An asymptote is a line that a curve approaches, getting closer and closer, but does not cross. Some definitions state that the curve may cross, but may not cross an infinite number of times. In the case of a rectangular hyperbole, the asymptotes are parallel or equal to the X and Y axes.

There are many different kinds of fractions, some rational and some irrational.

Some rational numbers are whole numbers, some are not. The set of whole numbers is a proper subset of rational numbers.