Discovering Transformations of Functions
Below you will find three graphs of functions. Use the check boxes to view each function. Adjust the sliders on the right to see how each coefficient affects both the function's equation and its graph. Then answer the questions below.
1. How does slider "a" affect f(x)? Is this result the same for g(x) and h(x)? 2. How does slider "d" affect the functions? 3. Show f(x) only. Leave slider "c" at 0, and make slider "b" 2. How did the x-value of points A, B and C change? now move slider "b" to 0.5. How are the x-values of the coordinates affected now? Lastly, make slider "b" -2. How is the graph affected? Check these results with graphs g(x) and h(x). Are they the same? 4. Looking at any of the three functions, set slider "b" to 1 and change slider c. How does slider c affect the function's equation and graph? 5. Now move slider "b" to 2, and change slider "c" to 4. How does that affect the horzontal shift? 6. Move slider "b" to 0.5 and slider "c" to 2. How does this affect the horizontal shift?