Chapter 2.3, Problem 91AYU

To determine

The number of $x$ -intercepts can a function defined on an interval have if it is increasing on that interval.

Answer to Problem 91AYU

Solution:

It will give exa ctly one or none $x$ -intercepton that interval.

Explanation of Solution

Given:

It is asked to explain the number of $x$ -intercepts can a function defined on an interval have if it is increasing on that interval.

An $x$ -intercept of a graph is a point where the graph crosses the $x$ -axis. An $x$ -intercept occurs at a point on the graph where the $y$ -coordinate is zero, (a.0).

A graph can have many intercepts, one intercept, or no intercepts. If the graph is the graph of a function then it has at most one $y$ -intercept, since the graph of a function must pass the vertical line test and the $y$ -axis is one such vertical line.

The graph of a function can have any number of $x$ -intercepts, including none and infinitely many.

It is given here that the function is increasing on that interval. As it is increasing on that interval, it will give exa ctly one or none $x$ -intercept.