Describe the shape of the graph of the cubic function by determining the end behavior and number of turning points.

Question

y=4x^3-3

Answer 1

The given cubic function is y = 4x^3 - 3.

End behavior:
The leading term in the function is 4x^3, which means that as x approaches positive infinity, the function also approaches positive infinity. And as x approaches negative infinity, the function approaches negative infinity. This indicates that the graph of the cubic function will have opposite end behavior on either side of the y-axis.

Number of turning points:
Since the degree of the polynomial is 3, we expect there to be 3 turning points on the graph of the cubic function.