Applet Prompts
The following are possible prompts that could accompany the applet:
1. Play around with the applet, particularly the check boxes for “rising” and “falling.” What is the relationship between the number of intervals where a function rises/falls versus the type of function it is (that is, quadratic, cubic, etc.)? Explain your reasoning.
2. Now play around with the “concave” and “convex” check boxes. What does it mean for a portion of a function to be concave? Convex? Explain your reasoning.
3. What does the inflection point (the blue cyan point) represent? How do you know?
4. What do the purple points represent? Explain your reasoning.
5. How does each slider value (a, b, c, and d) affect the graph of the function? Focus on positive and negative values as well as 0.
6. What other characteristics of polynomial functions can you think of that are not mentioned in this applet?
7. What type of functions (linear, quadratic, and cubic) can be odd functions? Even functions? Explain your reasoning.
1. Play around with the applet, particularly the check boxes for “rising” and “falling.” What is the relationship between the number of intervals where a function rises/falls versus the type of function it is (that is, quadratic, cubic, etc.)? Explain your reasoning.
2. Now play around with the “concave” and “convex” check boxes. What does it mean for a portion of a function to be concave? Convex? Explain your reasoning.
3. What does the inflection point (the blue cyan point) represent? How do you know?
4. What do the purple points represent? Explain your reasoning.
5. How does each slider value (a, b, c, and d) affect the graph of the function? Focus on positive and negative values as well as 0.
6. What other characteristics of polynomial functions can you think of that are not mentioned in this applet?
7. What type of functions (linear, quadratic, and cubic) can be odd functions? Even functions? Explain your reasoning.