Question

what can you say about the continuous function that generated the following table of values?
a. the function has no x - intercepts.
b. the function has more than one x - intercept.
c. the function has at least one x - intercept.
d. there is not enough information to answer the question.

Explanation:

The function is continuous. At \(x=-2\), \(y=-0.625\) (negative); at \(x=0\), \(y=0.5\) (positive). By the Intermediate Value Theorem, since the function crosses from negative to positive between \(x=-2\) and \(x=0\), it must have at least one \(x\)-intercept in this interval.

Answer:

C. The function has at least one x-intercept.