(a)

The cubic function is .

To find the -intercept substitute in function.

Thus, the cubic function intersects the -axis in one and only one point.

Statement (a) true.

(b)

Since the polynomial is a cubic polynomial it intersects the -axis at most three points.

Statement (b) true.

(c)

The polynomial is a cubic polynomial so it has atleast one -intercept.

Statement (c) true.

(d)

For  is very large, the function behaves like leading coefficient of the function.

Here the leading coefficient is .

Thus, the function behave like as the graph of . 

Statement (d) true.

(e)

The cubic function is .

Let and .

Substitute and in above equation.

Here the graph varies with respect to value.

If then the function is .

Graph :

Graph the function .

Observe the above graph it is not symmetry with respect to the origin.

Statement (e) is false.

(f)

The graph varies with respect to value.

Observe the above graph, the curve not passe through the origin.

The curve passes through the origin if .

Statement (f) is false.

(a) Statement (a) true.

(b) Statement (b) true.

(c) Statement (c) true.

(d) Statement (d) true.

(e) Statement (e) is false.

(f) Statement (f) is false.