Question

Which of the following graphs could represent a cubic function?

Answer 1

Answer:

A function is called cubic function if highest degree of polynomial containing one variable is 3.

And if you draw the graph of Cubic function in wo dimensional coordinate plane, it will cut x axis at three points.

A cubic polynomial has either 1 real root , 2 real root , or all real root. As imaginary root occur in pairs, so the cubic function has either 1 real root ,when 2 roots are non real, 2 real or all real root.

As, graph A , cuts X axis at one point , that is At , x=0 only.As, it can have all roots equal to 0 or 2  non real roots which are imaginary.It is the curve, y=x³

Similarly,  graph B , cuts X axis at one point , that is At , x=0 only, it is the graph of parabola.so there are no chances that it will cross the X axis again.

When, you look at the graph C, it cuts X axis at three points, so it could be graph of cubic polynomial.

Curve D , represents a straight line.

Option A as well as Option C, are graphs of cubic polynomial.

Answer 2

The answer would be graph (A)
The equation for this function is,
$f(x) = {x}^{3}$
Once you find different points around the graph it will end up looking like graph (A)

Hope this helped
:D