How is a rational function the ratio of two polynomial functions?

Updated: 4/28/2022
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That's the definition of a "rational function". You simply divide a polynomial by another polynomial. The result is called a "rational function".

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Q: How is a rational function the ratio of two polynomial functions?
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What is a rational equation or rational function?

It is any function which can be written as the ratio of two polynomial functions.

What is a rational function?

In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions. Neither the coefficients of the polynomials nor the values taken by the function are necessarily rational numbers.In the case of one variable, , a function is called a rational function if and only if it can be written in the formwhere and are polynomial functions in and is not the zero polynomial. The domain of is the set of all points for which the denominator is not zero, where one assumes that the fraction is written in its lower degree terms, that is, and have several factors of the positive degree.Every polynomial function is a rational function with . A function that cannot be written in this form (for example, ) is not a rational function (but the adjective "irrational" is not generally used for functions, but only for numbers).An expression of the form is called a rational expression. The need not be a variable. In abstract algebra the is called an indeterminate.A rational equation is an equation in which two rational expressions are set equal to each other. These expressions obey the same rules as fractions. The equations can be solved by cross-multiplying. Division by zero is undefined, so that a solution causing formal division by zero is rejected.

What about rational functions creates undefined and asymptotic behavior?

A rational function is the ratio of two polynomial functions. The function that is the denominator will have roots (or zeros) in the complex field and may have real roots. If it has real roots, then evaluating the rational function at such points will require division by zero. This is not defined. Since polynomials are continuous functions, their value will be close to zero near their roots. So, near a zero, the rational function will entail division by a very small quantity and this will result in the asymptotic behaviour.

Does transcendental mean it is equal to the ratio of two integers in math?

yes * * * * * No it does not. A transcendental number is not rational. It is irrational but, further than that, it is not the root of any polynomial equation with rational coefficients.

What causes the graph of a rational function to have a vertical asymptote?

When your input variable causes your denominator to equal zero. * * * * * A rational function of a variable, x is of the form f(x)/g(x), the ratio of two functions of x. Suppose g(x) has a zero at x = x0. That is, g(x0) = 0. If f(x0) is not also equal to 0 then at x = x0 the rational function would involve division by 0. But division by 0 is not defined. Depending on whether the signs of f(x) and g(x) are the same or different, as x approaches x0 the ratio become increasingly large, or small. These "infinitely" large or small values are the asymptotes of the rational function at x = x0. If f(x0) = 0, you may or may not have an asymptote - depending on the first derivatives of the two functions.

Which best describes pi?

π is a transcendental number which is defined to be the ratio between the diameter and circumference of any circle. (A transcendental number is a number which is not a root of a non-zero polynomial with rational coefficients.)

Is 0.25 irrational or rational?

0.25 is the ratio of 25 to 100. That's rational.

Is 26 rational or irrational?

2.6 is the ratio of 26 to 10 ... nice and rational.

What is the second degree polynomial that creates the golden ratio?

The polynomial equation is x2 - x - 1 = 0.

Is 17 irrational or rational?

17 is the ratio of 17 and 1 ... nice and rational.

What is the relationship between a ratio and rational numbers?

A rational number is one which can be expressed as a ratio of two integers.

Is 67 percent a rational number?

Yes. 67/100 is a ratio (fraction) Since it can be put into a ratio, it is a rational number.