Zero - Function

Any input value in the domain of a function whose output equals 0 is known as a zero or root of the function. A function can have more than one zero or no zeros at all. Graphically, the zeros of a function are the x coordinates of the x-intercepts.

Consider the following function as an example. f(x) = 2x+1 To find the zeros of a function, substitute the 0 for the output f(x) in the function rule and solve the resulting equation for x.

This example function has a zero at x=- 12 because f(- 12)=0. This can be verified by evaluating the function at this value.

Since this is the only solution to the equation, it is also the only zero of the function. If a function does not intercept the x-axis, there will be no real solution for the resulting equation when the function rule is set equal to 0. In such a case, the function will have no zeros.