Root of a function

Definition: A root of a function is an x-value at which the y-value is zero.

Rules:

Let y=f(x) be a function. Then x=a is a root if f(a)=0 .
If x=a is a root of f(x) , then the graph of f(x) crosses the x-axis at a.
So a root is an x-intercept.
The x-axis is also the line y=0. So substituting y=0 and solving for x gives roots.

Example: Find the roots of the quadratic function f(x)= x^2-x-2 .

To find the roots of a quadratic function, we use the quadratic formula.

The roots are: x_1=2 and x_2=-1

That is, this function crosses the x-axis at 2 points: (2,0) and (-1,0).

y=-x+2	y=-x^2+2x-1	y=2^x	f(x)=sinx
1 root	1 roots	0 roots	infinitely many roots
root: x=2	root: x=1	-	roots: \left\{ {x\|x = k\pi ,\,\,k \in \bf{Z}} \right\}

linear function ?	quadratic function	exponential function ?	trigonometric function ?

Add Comment
Sign as Author