Example of Determining the Domain of the Rational Function
To find the domain of the rational function , determine which values make the denominator equal to zero and exclude them.
Step 1. Set the denominator equal to zero: .
Step 2. Solve the equation. Begin by factoring out the greatest common factor: . Then, factor the trinomial: . Apply the Zero Product Property by setting each variable factor to zero: or . Solving these equations gives and .
Step 3. State the domain by excluding the values found in Step 2. Thus, the domain of is all real numbers where and .
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.7 Rational Expressions and Functions - Intermediate Algebra @ OpenStax
Algebra
Related
Example of Determining the Domain of the Rational Function
Example of Determining the Domain of the Rational Function
An operations manager is using a rational function to model the average cost per unit for a manufacturing process. To ensure the model is valid, the manager must determine the function's domain. Arrange the following steps in the correct order to determine the domain of a rational function.
A software developer is writing a validation script to ensure that a calculation tool handling rational functions does not crash due to a 'Division by Zero' error. To identify the specific values that must be excluded from the domain, which part of the rational function should the developer set equal to zero first?
Domain Validation Procedure in Software Quality Assurance
A financial analyst is using a rational function to model the growth rate of a startup. True or False: After identifying the specific values that make the denominator of the function equal to zero, the final step in determining the domain is to state that the domain consists only of those specific values.
An IT documentation specialist is drafting a troubleshooting guide for a logistics application that uses rational functions to calculate delivery windows. To help users understand why certain inputs are restricted, the specialist must outline the standard mathematical procedure for finding the domain. Match each step of this procedure to its correct description.
A data processing specialist is documenting the error-prevention steps for an algorithm that uses rational functions to compute production rates. To accurately determine the domain and prevent calculation errors, the standard procedure states that the very first step is to set the ________ expression equal to zero.
Drafting an SOP for Domain Verification
Example of Determining the Domain of the Rational Function
Learn After
An Environmental Safety Officer is using the mathematical model R(x) = rac{4x^2 - 16x}{8x^2 - 16x - 64} to monitor chemical concentration levels, where represents the temperature in degrees Celsius. To prevent equipment failure at temperatures where the model becomes undefined, the officer must determine the function's domain. Arrange the following steps in the correct order to find the domain for this specific function.
A telecommunications analyst uses the rational function R(x) = rac{4x^2 - 16x}{8x^2 - 16x - 64} to model signal interference across different frequencies (in gigahertz). To identify the frequencies where the model becomes undefined, the analyst must determine which values of result in a denominator of zero. Based on the analysis of this specific function, which pair of values causes the denominator to be zero?
A Quality Control Analyst uses the rational function R(x) = rac{4x^2 - 16x}{8x^2 - 16x - 64} to monitor the vibration frequency of a specialized turbine. To find the domain of this model, the analyst must identify the specific components of the denominator. Match each part of the domain-finding process for this specific function with its correct mathematical representation based on the provided example.
An urban planner uses the rational function to analyze traffic flow density at various intersections. True or False: Based on the domain analysis of this function, the value is an excluded value because it results in a denominator of zero.
Identifying Model Limitations in Logistics
A financial analyst uses the rational function to model the risk-to-reward ratio of an investment over time (in months). The model becomes undefined when the denominator is zero. When determining the domain of this function, solving the equation results in two excluded values. The positive value that must be excluded from the domain is ____.
Auditing the Domain Analysis of a Mathematical Model