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. Graphically, the zeros of a function are the x coordinates of the x-intercepts.
The function 0.4*(x+2)*(x-1)*(x-2) with zeros at (-2,0), (1,0), and (2,0)
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.
f(x)= 2x+1
0=2x+1
Solve for x
-1 = 2x
-1/2=x
-1/2=x
x=-1/2
This example function has a zero at x=- 12 because f(- 12)=0. This can be verified by evaluating the function at this value.
f(x)=2x+1
Evaluate
f( -1/2)=2( -1/2)+1
f(-1/2)=-1 +1
f(-1/2)=0
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.
Zeros of different functions applet
Exercises