1. Can the graph of a polynomial function have no y-intercept? Explain, provide a concrete example, and solve your example to prove the question.

2. Can the graph of a polynomial function have no x-intercept? Explain, provide a concrete example, and solve your example to prove the question.

3. Find at least two distinct polynomials, not of the same degree that has the following characteristics:

• Assume k = -1
• Crosses the x-axis at -1 and 4
• Touches the x-axis at 0 and 2 and is above the x-axis between 0 and 2
• Do both polynomials have the same number of turning points? Please explain. Determine the maximum number of turning points. Show work.

4. Find at least two distinct polynomials, not of the same degree that has the following characteristics:

• Assume k = 1
• Crosses the x-axis at -2
• Touches the x-axis at 1 and is above the x-axis between -2 and 1
• Do both polynomials have the same y-intercept? Please explain
• Do both polynomials have the same number of turning points? Please explain. Determine the maximum number of turning points. Show work.