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Zero - Function
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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.
Solve for x
This example function has a zero at because 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 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