The end behavior of the cubic function y = 2x^3 - 4x - 3 can be determined by looking at the coefficient of the highest power term, which is 2x^3. Since the coefficient is positive, the graph will rise to positive infinity on the right side and fall to negative infinity on the left side.
To determine the number of turning points, we can find the derivative of the function and count the number of places where the derivative changes sign. The derivative of y = 2x^3 - 4x - 3 is y' = 6x^2 - 4.
Setting the derivative equal to zero, we get 6x^2 - 4 = 0. Solving this equation, we find x^2 = 2/3, and therefore, x = ±√(2/3).
Since the discriminant is positive, there are two distinct real roots. We then have two turning points: one where the graph changes from decreasing to increasing at x = -√(2/3), and another where the graph changes from increasing to decreasing at x = √(2/3).
Therefore, the graph of the cubic function y = 2x^3 - 4x - 3 has two turning points.
Describe the shape of the graph of the cubic function by determining the end behavior and number of turning points.
y=2x^3-4x-3
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