Question

Select all the statements below that are true of the following graph of the polynomial.

Answer 1

To find:

We need to comment on the following points of the given graph:

Step by step solution:

1) Type of function (odd / even):

If the function is odd then the graph is symmetrical about the origin.

Upon observing this graph we can see that the given graph is symmetrical about the origin, So it is an odd function.

2) To check whether (x-2) is a factor of the equation:

If (x-2) is the factor of the equation, then x = 2 should be the root of the the equation

Upon observing the graph, we can see that the graph cut the x axis at x = 2, So (x-2) is the factor of the equation.

3) To check whether there are 5 zeroes or not:

If there are 5 zeroes of the graph, the graph should cut the x - axis for 5 times.

Upon observing the graph we can see that the graph cut the x - axis for 5 times, thus it has 5 zeroes.

4) To check whether there are same amount of relative minimums as relative maximums:

Upon observing the graph we can see that there are 2 relative minimums and 2 relative maximums.

So we can see that there are same amount of relative maximums and minimums.

5) To check whether there is a relative minimum at (-1,-3)

To have a relative minimum at (-1,-3) there should be a minima at (-1,-3)

Upon observing the graph we can see that there is no minima at (-1,-3), So it there is no relative minimum at (-1,-3)

From here we can say that, 1,2,3,4 are the 4 correct options for this equation.