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Determining if an Equation Defines a Function
To determine whether an equation in two variables defines a function (assuming is the independent variable and is the dependent variable), the systematic procedure is to algebraically solve the equation for . Then, test the equation by substituting a specific numerical value for . If each value substituted for results in exactly one corresponding value for , the equation defines a function. Conversely, if substituting a specific value for produces two or more distinct values for , the equation does not define a function because a single input cannot map to multiple outputs.
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Intermediate Algebra @ OpenStax
Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
Algebra
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Solving an Equation
Translating English Sentences into Equations
Algebraic Formula
Quadratic Equation
Radical Equation
Comparison of Algebraic Structure to English Grammar
In a corporate financial model, which term describes a mathematical statement that uses an equal sign (=) to show that two expressions, such as 'Total Revenue' and 'Price per Unit times Units Sold', represent the same value?
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Categorizing Automated Business Logic
Defining Algebraic Equations in a Professional Context
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Linear Equation in One Variable
Solution of an Equation
Standard Form of a Linear Equation
Determining if an Equation Defines a Function
Linear Equation in Two Variables
Absolute Value Equations
Learn After
Example: Determining if the Equation Defines a Function
Example: Determining if the Equation Defines a Function
Example: Determining if the Equation Defines a Function
Example: Determining if the Equation Defines a Function
Example: Determining if the Equation Defines a Function
Example: Determining if the Equation Defines a Function
Example: Determining if the Equation Defines a Function
Example: Determining if the Equation Defines a Function
Example: Determining if the Equation Defines a Function