How to Write Functions in Math

A line graph with only one y for every x is a function.
••• Ryan McVay/Photodisc/Getty Images

You can graph circles, ellipses, lines and parabolas and represent all these by equations in math. However, not all these equations are functions. In math, a function is an equation with only one output for each input. In the case of a circle, one input can give you two outputs - one on each side of the circle. Thus, the equation for a circle is not a function and you cannot write it in function form.

    Apply the vertical line test to determine if your equation is a function. If you can move a vertical line along the x-axis and only intersect one y at a time, your equation is a function as it follows the only one output for each input rule.

    Solve your equation for y. For instance, if your equation is y -6 = 2x, add 6 to both sides to get y = 2x + 6.

    Decide on a name for your function. Most functions use a one-letter name such as f, g or h. Determine what variable your function depends upon. In the example of y = 2x + 6, the function changes as the value of x changes, so the function is dependent upon x. The left side of your function is the name of your function followed by the dependent variable in parenthesis, f(x) for the example.

    Write your function. The example becomes f(x) = 2x + 6.


    • You write functions with the function name followed by the dependent variable, such as f(x), g(x) or even h(t) if the function is dependent upon time. You read the function f(x) as "f of x" and h(t) as "h of t". Functions do not have to be linear. The function g(x) = -x^2 -3x + 5 is a nonlinear function. The equation is nonlinear because of the square of x, but it is still a function because there is only one answer for every x. When evaluating a function for a specific value, you place the value in the parenthesis rather than the variable. For the example of f(x) = 2x + 6, if you wish to find the value when x is 3, you write f(3) = 12 since 2 times 3 plus 6 is 12. Similarly, f(0) = 6 and f(-1) = 4.


    • Do not confuse function names with multiplication. Function f(x) is not variable f times variable x. Function f(x) is a function named f that depends upon x.

Related Articles

How to Calculate Function From Ordered Pairs
How Do I Get the Theta Sign on My TI-84?
How to Explain Input & Output Tables in Algebra
How to Find the Domain of a Function Defined by an...
How to Find Zeros of Linear Functions
How to Find Y Value for the Slope of a Line
How to Calculate Function From Ordered Pairs
How to Calculate Instantaneous Rate
How to Solve for a Variable in a Trig Function
How to Determine Whether the Relation is a Function
What is the Vertical Line Test?
To Calculate Arcsine, What Buttons Do You Press on...
What Are Double Angle Identities?
How to Find X & Y Intercepts on a Graphing Calculator
How to Solve a Parabola
How to Find Correlation Coefficient & Coefficient of...
How to Graph Parabolas on a TI-84 Calculator
How to Find the X Intercept of a Function
Ways to Tell if Something Is a Function

Dont Go!

We Have More Great Sciencing Articles!