Question

part a. can the graph have an x - intercept?
a. yes
b. no

Explanation:

Step1: Recall the definition of x - intercept

An x - intercept is a point where the graph of a function crosses the x - axis. At this point, \(y = 0\).

Step2: Consider the properties of a function negative over an interval

A function \(y = f(x)\) is negative over an interval \((a,b)\) if \(f(x)<0\) for all \(x\in(a,b)\). But the x - intercept occurs when \(y = f(x)=0\). For example, consider a continuous function. By the Intermediate Value Theorem, if a function is defined on an interval that includes a point where it could cross the x - axis (even if it is negative over most of an interval), it is possible to have an x - intercept. For a non - continuous function, we can also construct a function that is negative over most of its domain but has an x - intercept.

Answer:

A. Yes