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Zero - Function

Concept

Zero - Function

To find where a function intercepts the xx-axis, the function can be set equal to zero. Then, the x-x\text{-}values that satisfy the equation are the zeros of the function, also called the roots. f(x)= 2x+10= 2x+1x= -0.5\begin{aligned} f(x) =&\ 2x+1 \\ 0 =&\ 2x+1 \\ x =&\ \text{-}0.5 \end{aligned} This example function has the zero x=-0.5,x=\text{-}0.5, since f(-0.5)=0.f(\text{-}0.5)=0. Functions whose degree is greater than one, such as quadratic functions, may have more than one root. f(x)=x24\begin{gathered} f(x)=x^2-4 \end{gathered} This function has the zeros x=2x=2 and x=-2,x=\text{-}2, since the function will evaluate to 00 if either of these values is substituted for x.x. f(x)=x24f(x)=x24f(2)=224f(-2)=(-2)24f(2)=0f(-2)=0\begin{array}{c|c} f(x)=x^2-4 & f(x)=x^2-4\\ f(2)=2^2-4 & f(\text{-}2)=(\text{-}2)^2-4 \\ f(2)=0 & f(\text{-}2)=0 \end{array} If a given function doesn't intercept the xx-axis, there will be no solution when the function is equal to 0.0.
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