# Parent Functions of Rational Functions

• ABC_123
In summary, parent functions refer to a set of basic functions that are commonly used as building blocks in mathematical equations. These include f(x)=x, f(x)=x^2, f(x)=sqrt(x), f(x)=1/x, and f(x)=|x|. The parent function for Rational functions is not as commonly recognized, but it can be understood as any function that is not integrated or derived. It is important to avoid typing in all caps as it can cause discomfort for others. If you encounter this, you can report it for resolution.
ABC_123
what is the precise definition of "parent functions" ?

I know that : f(x)=x ,f(x)=x^2 , f(x)=sqr(x) , f(x)=1/x , f(x)=|x| are parent functions but what about Rational functions?
what is the parent function of the Rational functions ?

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never heard of them.

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Do you perhaps mean functions that have not yet been integrated or derived?

Also, please don't type in all caps. It's giving me a headache.

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Hobin said:
Also, please don't type in all caps. It's giving me a headache.

You can always report these things. I'll remove the caps.

micromass said:
You can always report these things. I'll remove the caps.

I didn't know that, I'll keep it in mind.

## 1. What is a rational function?

A rational function is a mathematical function that can be expressed as the ratio of two polynomial functions. It has the general form of f(x) = p(x)/q(x), where p(x) and q(x) are polynomial functions and q(x) is not equal to 0.

## 2. What are some common parent functions of rational functions?

Some common parent functions of rational functions include the reciprocal function (f(x) = 1/x), the square root function (f(x) = √x), and the cube root function (f(x) = ³√x).

## 3. How do you identify the parent function of a rational function?

To identify the parent function of a rational function, you can look at the highest degree of the numerator and denominator. The parent function will have the same degree for both the numerator and denominator. For example, if the rational function has a numerator of x^2 and a denominator of x^3, the parent function would be f(x) = x^2/x^3 = 1/x.

## 4. What is the domain of a rational function?

The domain of a rational function is all real numbers except for any values that would make the denominator equal to 0. This is because dividing by 0 is undefined in mathematics. Therefore, the domain of a rational function is all real numbers except for the values that would make the denominator equal to 0.

## 5. How do you graph a rational function?

To graph a rational function, you can start by finding the x-intercepts and y-intercepts by setting the numerator and denominator equal to 0. Then, plot these points on a graph and draw a curve that passes through them. You can also use the parent function to determine the general shape and behavior of the graph, such as the end behavior and any asymptotes.

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