Chapter 3, Problem 25MCQ

To determine

Toexplain:The relationship between x-intercepts of a graph and the zeroes of the function.

Answer to Problem 25MCQ

On a graph for a function $y=f\left(x\right)$ , x-intercepts define the points at which $y=0$ and zeroes are the roots of the function i.e. x coordinates where value of y is zero. Thus both represent the same thing.

Explanation of Solution

Consider a function $y=f\left(x\right)$ , for this function the zeroes are the values of $x$ for which the value of function is zero. These are also called the roots of the function.If $p$ is the zero or root of the function $y=f\left(x\right)$ , the value of function for $p$ , $f\left(p\right)=0$ .

While the x-intercepts are the points on the graph drawn on the Cartesian plane for which the value of $y=0$ . The x-intercepts occur at $f\left(p\right)=0$ , here $p$ is the root of the function under consideration.

Therefore, on a graph for a function $y=f\left(x\right)$ , x-intercepts define the points at which $y=0$ and zeroes are the roots of the function. Thus both of them represent the same concept. One term i.e. intercepts is widely used in coordinate concept and second term i.e. zeros are used in algebraically.