Question

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

B.

C.

D.

Answer 1

Hint: To find the correct solution of this problem assume a simple cubic function $y = {x^3}$, now draw a graph using this equation. The obtained graph will match with the correct solution to the question.

Complete step-by-step solution -
Let us take a simple cubic function $y = {x^3}$ to plot the graph.
First let x =1
then Y=1
When x=2
then Y= ${2^3}$
Y = 8
Similarly, when x=3
Y=${3^3}$
Y=27
Do this procedure and make a table to record the data

X	1	2	3	4	5	6
Y	1	8	27	64	125	216

Similarly repeat the process with negative numbers i.e.
when x= -1
Y=-1
When x=-2
x=-8
When x= -3
Y=-27
By continuing we get

X	0	-1	-2	-3	-4	-5	-6
Y	0	-1	-8	-27	-64	-125	-216

Now use the data above from table 1 and table 2 to plot a graph which would look like this

This graph can change since a cubic function is of the form $Y = a{x^3} + b{x^2} + cx + d$ as the variables are added the more complex the graph can be but as you can see the graph is similar to that of Option B and Option D. Thus, Option B and D are graphs of cubic Function. You can also determine this simply by analyzing the graph and using elimination methods.
In Graph A, there is no solution to the problem since the graph doesn’t intersect the x and Y axis.
Similarly in Graph C the graph is a straight line and we know that straight lines always have linear equations.

Note: In the above solution we used the concept of graph which can be explained as a common method of visually explaining relationships in data. The aim of a graph is to present data that are too numerous or complicated to be adequately represented in text and in less space.