Get the free 9.3 - Graphing Rational Functions - www2 hoover k12 al

This document provides a comprehensive overview on graphing rational functions, including definitions, methods to find asymptotes and holes, and example problems with graphical representations.

How to fill out 93 - graphing rational

How to fill out 9.3 - Graphing Rational Functions

1. Begin by identifying the rational function you need to graph, in the form of f(x) = P(x)/Q(x), where P and Q are polynomials.
2. Determine the domain of the function by finding the values of x that make the denominator Q(x) equal to zero, as these values are not included in the domain.
3. Find the intercepts of the graph by setting f(x) to zero to get the x-intercepts (roots) and evaluating f(0) for the y-intercept.
4. Analyze the asymptotes: find vertical asymptotes by setting Q(x) to zero and horizontal asymptotes by comparing the degrees of P(x) and Q(x).
5. Evaluate the function at several critical points, especially around intercepts and asymptotes, to understand the behavior of the function.
6. Plot the intercepts, asymptotes, and points found in step 5 on a graph.
7. Draw the graph of the rational function, ensuring to show the behavior approaching the asymptotes and through the intercepts.

Who needs 9.3 - Graphing Rational Functions?

1. Students learning algebra and precalculus concepts.
2. Teachers or tutors who are instructing students on graphing functions.
3. Anyone needing to understand the behavior of rational functions for higher mathematics courses.
4. Professionals in fields that require data analysis or mathematical modeling involving rational functions.

People Also Ask about

How to graph linear rational functions?

Graphing a Rational Function in Linear Over Linear Form Step 1: Find a vertical asymptote. Step 2: Find a horizontal asymptote. Step 3: Find the -intercepts and the -intercepts. Step 4: Make a table of and values. Step 5: Plot the intercepts and the points in the table.

What are 5 examples of rational functions?

How To: Given a linear function, graph by plotting points. Choose a minimum of two input values. Evaluate the function at each input value. Use the resulting output values to identify coordinate pairs. Plot the coordinate pairs on a grid. Draw a line through the points.

What are the steps for graphing a rational function?

Steps for Graphing Rational Functions Find the x- and y-intercepts of the graph of y=r(x), if they exist. Determine the location of any vertical asymptotes or holes in the graph, if they exist. Analyze the behavior of r on either side of the vertical asymptotes, if applicable. Analyze the end behavior of r.

How to graph rational functions step by step?

Examples of rational functions include: f(x)=1x f ( x ) = 1 x , f(x)=5x−3x2−1 f ( x ) = 5 x − 3 x 2 − 1 , h(x)=x2−5x3+2x2+7 h ( x ) = x 2 − 5 x 3 + 2 x 2 + 7 , g(x)=7x3−5xx2−5 g ( x ) = 7 x 3 − 5 x x 2 − 5 .

How do you solve rational functions step by step?

The steps to solving a rational equation are: Find the common denominator. Multiply everything by the common denominator. Simplify. Check the answer(s) to make sure there isn't an extraneous solution.

How do you graph a function step by step?

How To: Given a linear function, graph by plotting points. Choose a minimum of two input values. Evaluate the function at each input value. Use the resulting output values to identify coordinate pairs. Plot the coordinate pairs on a grid. Draw a line through the points.

For pdfFiller’s FAQs

What is 9.3 - Graphing Rational Functions?

9.3 - Graphing Rational Functions is a mathematical technique that involves plotting the graphs of functions that are expressed as the ratio of two polynomials.

Who is required to file 9.3 - Graphing Rational Functions?

Typically, students in algebra or calculus courses who are studying graphing techniques for rational functions will engage with this material; it may not be a filing requirement but rather an educational exercise.

How to fill out 9.3 - Graphing Rational Functions?

To fill out 9.3 - Graphing Rational Functions, one must identify the function, determine key characteristics such as intercepts, asymptotes, and behavior at infinity, and plot these points on a graph.

What is the purpose of 9.3 - Graphing Rational Functions?

The purpose of 9.3 - Graphing Rational Functions is to help students visualize and understand the behavior of rational functions and to facilitate the solving of equations involving these functions.

What information must be reported on 9.3 - Graphing Rational Functions?

Information that must be reported includes the equation of the rational function, intercepts, asymptotes, domain and range, and significant points on the graph.