Question

Select the correct answer. Describes the zeros of the graphed function.

Answer 1

The function has 3 distinct roots (OPTION A)

SOLUTION

Problem Statement

The question gives us a graph and we are required to find the number of zeros the function has.

Method

- The number of zeros a function has corresponds to the number of times the graph crosses the x-axis. If the graph crosses the x-axis once then there is one zero. If it crosses the x-axis twice, then it has 2 zeros.

- The number of zeros a function has also depends on the way the graph touches the x-axis. If the graph touches the x-axis like a quadratic, then there are 2 zeros or zeros that are multiples of 2, that have the same value.

Implementation

The following can be observed from the figure given to us:

- The graph crosses the x-axis twice at x = -2 and x = 2. This means that the graph has at least 2 zeros.

- The graph curves like a quadratic at x = 0. This means that there are at least 2 zeros of the same value or zeros of the same value.

Thus, we can predict that the function must be:

`x^2\mleft(x-2\mright)\mleft(x+2\mright)`

Final Answer

The answer is:

The function has 3 distinct roots (OPTION A)