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Zero - Function
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Concept

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. The zeros of a function are found graphically at its x-intercepts.
Function with three zeros
Consider the following function as an example.
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.
f(x)=2x+1
0=2x+1
Solve for x
-1=2x
This example function has a zero at because This can be verified by evaluating the function at this value.
f(x)=2x+1
Evaluate
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 solution for the resulting equation when the function rule is set equal to 0. In such a case, the function will have no zeros.
Zeros of different functions applet
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