Question

Describe and correct the error a student made in finding the​ interval(s) over which the function is positive and negative.

LOADING... Click the icon to view the​ student's work.

Choose the correct answer below.

A.

The zeros are neither positive nor negative. The student included these in the interval over which the function is​ negative, which is incorrect.

B.

The zeros are both positive and negative. The student included these in the interval over which the function is positive but not in which the function is​ negative, which is incorrect.

C.

The zeros are neither positive nor negative. The student included these in the interval over which the function is​ positive, which is incorrect.

D.

The zeros are negative. The student included these in the interval over which the

Answer 1

The zeros are neither positive nor negative. The student included these in the interval over which the function is​ positive, which is incorrect.

Get that A! ;p

Answer 2

The segments nor the graph are shown here, so i will answer in the most general way that i can.

First, for definition, a positive number A is such that:

A > 0

And a negative number B is such that:

B < 0.

Then, 0 is neither positive nor negative.

Now, if we have two consecutive zeros in a function (and the function is continuous) between these points the function can be only negative or positive (The function must be zero at some point in order to change of sign)

But notice that if f(x) is positive between x1 and x2, and f(x1) = 0, f(x2) = 0, we have that the segment where f(x) is positive is written as:

(x1, x2)

Where the (,) symbols mean that the values in the extremes do not belong to the segment.

Now, i can not see the segments that the student found.

If in the segment the function is negative, then the correct option is A (the function is negative in this segment if the graph of the function is under the x-axis in this segment)

If in the segment the function is positive, then the correct option is C (the function is positive in this segment is the graph of the function is above the x-axis in this segment)