Question

Which of the following is the graph of a cubic function.

Answer 1

Hint: According to given in the question we have to choose the graph of a cubic function which can be determined by the process as mentioned below:
As we know that if the ray touches the x-axis which is a horizontal line (as given in the options) at a one point then it is known as a linear function and when the ray touches the x-axis which is a horizontal line (as given in the options) at two points then it is known as a quadratic function and same as if the ray touches the x-axis which is a horizontal line (as given in the options) at three points then it is known as a cubic function.
Hence, with the help of the process given above we can determine the correct option or cubic function.

Complete step-by-step answer:
Step 1: First of all let’s consider the first graph given in the option (A) which is:

As we can see that the ray does not touch at any point on the x-axis so as explained in the solution hint we can say that this is not a cubic function, so option (A) is not correct.
Step 2: Now, we have to consider the graph 2 in the option (B) which is:

Now, as we can see that the ray touches the x-axis at three points so three zeroes or three roots will be obtained hence, we can say that the given function is a cubic function so, option (B) is correct.
Step 3: Same as step 2, we have to consider the graph 3 in the option (C) which is:

Now, as we can see that the ray touches the x-axis at one point so only one zero or one root will be obtained hence, we can say that the given function is a linear function so option (C) is not correct.
Step 4: Now, same as step 1,2, and 3, we have to consider the graph 4 in the option (D) which is:

Now, as we can see that the ray touches the x-axis at two points so two zeroes or two roots will be obtained hence, we can say that the given function is a quadratic function so, option (D) is not correct.

Hence, by finding the roots or zeros of the given function according to the process as mentioned in the solution hint we have obtained the cubic function or the correct option which is (B).

Note: If the ray cuts the x-axis at no point then it’s not a function and if a ray cuts the x-axis at one point then the given function is linear function, if the ray cuts the x-axis at two points then the function is quadratic function and same as if the ray cuts the x-axis at three points then the function is cubic function.
If the ray cuts the x-axis at no point then there is no any root of the function and if a ray cuts the x-axis at one point then there is only one root of the function, if the ray cuts the x-axis at two points then there are two roots of the function and same as if the ray cuts the x-axis at three points then there are three roots of the function.