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Elimination Using Multiplication
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Working with Percentages and Proportions
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Simplifying Complex Fractions
Dividing Whole Numbers with Long Division
Solving Compound Linear Inequalities
Raising a Quotient to a Power
Solving Rational Equations
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Adding with Negative Numbers
Quadratic Inequalities
Dividing Monomials
Using the Discriminant in Factoring
Solving Equations by Factoring
Subtracting Polynomials
Cube Root
The Quadratic Formula
Multiply by the Reciprocal
Relating Equations and Graphs for Quadratic Functions
Multiplying a Polynomial by a Monomial
Calculating Percentages
Solving Systems of Equations using Substitution
Comparing Fractions
Solving Equations Containing Rational Expressions
Factoring Polynomials
Negative Rational Exponents
Roots and Radicals
Intercepts Given Ordered Pairs and Lines
Factoring Polynomials
Solving Linear Inequalities
Powers
Mixed Expressions and Complex Fractions
Solving Equations by Multiplying or Dividing
The Addition Method
Finding the Equation of an Inverse Function
Solving Compound Linear Inequalities
Multiplying and Dividing With Square Roots
Exponents and Their Properties
Equations as Functions
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Factoring Trinomials
Solving Quadratic Equations by Completing the Square
Dividing by Decimals
Lines and Equations
Simplifying Complex Fractions
Graphing Solution Sets for Inequalities
Standard Form for the Equation of a Line
Fractions
Checking Division with Multiplication
Elimination Using Addition and Subtraction
Complex Fractions
Multiplication Property of Equality
Solving Proportions Using Cross Multiplication
Product and Quotient of Functions
Adding
Quadratic Functions
Conjugates
Factoring
Solving Compound Inequalities
Operating with Complex Numbers
Equivalent Fractions
Changing Improper Fractions to Mixed Numbers
Multiplying by a Monomial
Solving Linear Equations and Inequalities Graphically
Dividing Polynomials by Monomials
Multiplying Cube Roots
Operations with Monomials
Properties of Exponents
Percents
Arithmetics
Mixed Numbers and Improper Fractions
Equations Quadratic in Form
Simplifying Square Roots That Contain Whole Numbers
Dividing a Polynomial by a Monomial
Writing Numbers in Scientific Notation
Solutions to Linear Equations in Two Variables
Solving Linear Inequalities
Multiplying Two Mixed Numbers with the Same Fraction
Special Fractions
Solving a Quadratic Inequality
Parent and Family Graphs
Solving Equations with a Fractional Exponent
Evaluating Trigonometric Functions
Solving Equations Involving Rational Expressions
Polynomials
Laws of Exponents
Multiplying Polynomials
Vertical Line Test
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Solving Inequalities with Fractions and Parentheses
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Multiplying Polynomials
Fractions
Solving Quadratic and Polynomial Equations
Extraneous Solutions
Fractions
 
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Vertical Line Test

You have seen that a function is a rule that assigns to each input number, x, exactly one output number, y. If a rule assigns more than one output value to a given input value then it is not a function.

If we are given a graph we can determine if it represents a function by using the vertical line test.

 

Procedure — To Determine if a Graph Represents a Function (Vertical Line Test)

If you can draw a vertical line anywhere through the graph and it intersects the graph only one time, then the graph represents a function.

Here are the graphs of four functions. Notice that no matter where you draw a vertical line, it will never cross the graph more than one time.

The graphs below do NOT represent functions. In each, we can draw a vertical line that intersects the graph more than once. This shows that a given value of the input, x, is assigned to more than one value of the output, y.

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