Consider the polynomial function f ( x ) = - 2 x ⁵ + x ³ - 2 x ² + 3 and answer the following questions:

1. What is the end behavior (long-run behavior) of this graph? That is what is f ( x ) approaching as x → ∞ and as x → - ∞ ? How would you know the answer to this without looking at the graph of the function? 

2. What is the maximum number of zeros (x-intercepts) this graph could possibly have based only on the equation. How would you make this determination without looking at the graph? 

3. What is the maximum number of turning points this graph could possibly have based only on the equation. How would you make this determination without looking at the graph?

4. Graph the function on your calculator. How many zeros (x-intercepts) and turning points does the graph actually have?

5. Create your own equation of a function that has the following properties. Write out the equation of your function and make a graph. The graph has 2 turning points, The function has 3 x-intercepts