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Name Date Class LESSON81Graphing Simple Rational Functions Practice and Problem-Solving: A/B1 as a guide, describe x the transformation and graph the function. Using the graph of f (x) 1. G (x) 2

How to fill out graphing simple rational functions

How to fill out graphing simple rational functions:

1. Start by identifying the numerator and denominator of the rational function. The numerator is the top part of the fraction and the denominator is the bottom part.
2. Determine any vertical asymptotes by setting the denominator equal to zero and solving for the variable. The values that make the denominator zero will be the vertical asymptotes.
3. Find any horizontal asymptotes by comparing the degrees of the numerator and denominator. If the degree of the numerator is greater than the degree of the denominator, there will be no horizontal asymptote. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote will be at the ratio of the leading coefficients. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote will be at y = 0.
4. Determine any holes in the graph by simplifying the rational function and canceling out common factors between the numerator and denominator. Any values that result in the denominator becoming zero and the simplified form having a non-zero value at that point will be considered a hole in the graph.
5. Use a table of values to plot points on the graph. Choose x-values that are close to the vertical asymptotes, zeros, or any other key points. Calculate the corresponding y-values by substituting the chosen x-values into the rational function.
6. Plot the identified points on the graph and connect them smoothly to create the curve of the rational function.

Who needs graphing simple rational functions:

1. Mathematics students studying functions and graphing: Graphing simple rational functions is an important skill for mathematics students as it helps in understanding the behavior and characteristics of these types of functions. It allows them to visually represent and analyze the relationship between variables in real-world situations.
2. Engineers and scientists: Rational functions are commonly used in engineering and scientific fields to model many phenomena. Being able to graph and interpret rational functions helps engineers and scientists to analyze and predict how variables are related and make informed decisions based on those relationships.
3. Financial analysts and economists: Rational functions are also used in finance and economics to analyze and forecast various economic variables such as interest rates, demand, or supply functions. By graphing rational functions, financial analysts and economists can visually interpret and analyze these relationships, making informed decisions and predictions in their respective fields.

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What is graphing simple rational functions?

Graphing simple rational functions involves creating a visual representation of mathematical functions that are ratios of two polynomials.

Who is required to file graphing simple rational functions?

Students studying mathematics or anyone interested in understanding the behavior of rational functions may be required to graph simple rational functions.

How to fill out graphing simple rational functions?

To fill out graphing simple rational functions, one must input the rational function equation, determine the domain and range, locate any vertical asymptotes, and plot points to create the graph.

What is the purpose of graphing simple rational functions?

The purpose of graphing simple rational functions is to visually represent the behavior of the function, including any asymptotes, intercepts, and end behavior.

What information must be reported on graphing simple rational functions?

Information such as the rational function equation, domain and range, asymptotes, intercepts, and key points on the graph must be reported on graphing simple rational functions.