Question

Which of the following graphs could represent a cubic function?

Answer 1

Graph A because it has two stationary points. That is, if you differentiate and put dy/dx as 0 there will be two answers

Answer 2

The graph that represents a cubic function is:

Graph A.

Explanation:

We know that for the graph of a cubic function it satisfies the property that:

• Both the ends of a graph must be in opposite directions.

• Also the graph attains the point of extrema at two points or zero point.

• Range is the set of real numbers.

• It has one inflection point.

• The graph has at least one real root.

Graph B:

It is a graph of a linear function.

Since a graph of a linear function is a straight line.

Graph C:

It is a graph of a quadratic function.

Since both the ends of the graph are in the same direction.

Graph D:

It is also a graph of a linear function.

As the graph is a straight line.

Graph A:

It is a graph of a cubic function.

Since it satisfies all the above properties.