In this module, you will be exploring piecewise functions. The red and blue sliders control the slope ( and ) and y-intercept ( and ) of f(x) (the red line) and g(x) (the blue line). The function h(x) is a piecewise function that has two pieces, the domain of each is determined by the green slider. Both h(x) and the green slider are currently toggled off. To toggle anything on or off, click the circle next to them on the left hand side (blue is toggled on and white is toggled off) Play around with the sliders, toggle the different functions and sliders on and off, and when you are comfortable, answer the questions below (you do not need to copy them)!
Before you start answering the questions, make sure f(x), g(x) and their sliders are toggled on and h(x) and the green slider are toggled off. Move the red and blue sliders so that f(x) and g(x) are not directly on top of each other. 1. What values do the red sliders change? How does this change the graph of the red line? 2. What values do the blue sliders change? How does this change the graph of the blue line? 3. Even though h(x) is toggled off, what do you notice happens to its functions as you slide the red and blue sliders? 4. The top function in h(x) is the same function as which, f(x) or g(x)? 5. The bottom function in h(x) is the same function as which, f(x) or g(x)? Toggle h(x) and the green slider on. 6. What do you notice about h(x) in relation to f(x) and g(x)? Toggle f(x) and g(x) off. 7. What happens when you move the green slider? What value in h(x) does the slider control? How does this change the graph of h(x)? 8. Moving all of the sliders around, is there any setting where h(x) fails the vertical line test? 9. Can you think of a reason why it would be useful to have h(x) instead of two individual functions like f(x) and g(x)? 10. Did this module help you understand piecewise functions? Be honest!