How to Find the Function in Math

Math

A function is a special mathematical relationship between two sets of data, where no member of the first set is directly related to more than one member of the second set. The easiest example to illustrate this is grades in school. Let the first set of data contain every student in a class. The second set of data contains every possible grade a student could receive. In order to satisfy the mathematical definition of a function, each student must receive exactly one grade. Not all the grades may be given, and some may be given more than once--for example, more than one student might get a 95 percent final grade. But no student receives more than one grade. The best way to find out whether an equation represents a function or not is by graphing the equation and then applying the vertical line test.

    Graph the two-variable equation on graph paper. For a straight line this means graphing two or more points on the line and connecting the dots. Methods for graphing other shapes may vary: Sometimes you can recognize the specific shape, and how to graph it, from its equation. Sometimes you just have to graph many points from the equation, selecting an x-value, finding the corresponding y-value and plotting that point on the graph. Then select a new x-value, find its corresponding y-value, graph that point, and continue on until you can get a feel for the shape.

    Draw a vertical line through any given point on the line or lines you graphed. Does it cross through the graph you drew at one point, or at more than one point? If it crosses through the graph at more than one point, this proves that the equation you're considering is not a function.

    Imagine running the vertical line you drew all the way to the left and all the way to the right of the graphed equation. Would it, at any point along the graph at all, intersect the lines at more than one point at once? If the answer is no, you've identified a function. If it's yes, you have proven that the equation does not represent a function.

    Things You'll Need

    • Pencil
    • Graph paper

Related Articles

How to Write a Prediction Equation for a Scatter Plot
How to Determine the Y-Intercept of a Trend Line
How to Find Equations of Tangent Lines
How to Find the X Intercept of a Function
How to Find Quadratic Equations From a Table
How to Find the Inverse of a Function
How to Find the Slope & the Equation of the Tangent...
How to Find the Slope in a Circle
How to Write Functions in Math
How to Find Y Value for the Slope of a Line
What is the Vertical Line Test?
To Calculate Arcsine, What Buttons Do You Press on...
How to Do Function Tables in 6th Grade Math
Facts About Functions for Algebra 1
How to Convert Graphs to Equations
How to Find X-Intercept & Y-Intercept
How to Find The Slope of a Line Given Two Points
How to Create Linear Equations
How to Find a Tangent Line to a Curve
How to Find the Point of Discontinuity in Algebra II

Dont Go!

We Have More Great Sciencing Articles!