Q. 91 - Precalculus Enhanced with Graphing Utilities

Question

How many x-intercepts can a function defined on an interval have if it is increasing on that interval? Explain.

Step-by-Step Solution

Answer

A function can be defined on an interval and increasing on that interval if it has at most one x-intercept.

Step 1. Given Information

The x-intercept is the point where a line crosses the x-axis. We have to find the x-intercepts where a function is defined on an interval and increasing on that interval.

Step 2. Explaining

Let's say that the function $f\left(x\right)$ is increasing on the interval $\left(x_1, x_2\right)$ and if the function has more than one x-intercepts, the function tends to decrease for some interval between $\left(x_1, x_2\right).$ Thus, a function can be defined on an interval and increasing on that interval if it has at most one x-intercept.