Function Transformations
We often explore four types of function translations: reflections across the x-axis, vertical stretches, horizontal shifts, and vertical shifts. For a function f(x), a translated function g(x) often takes the form g(x)=a f(x+b)+c. Explore the following functions, using the appropriate sliders, to determine how the values of a, b, and c define function translations for many functions.
Transform from f(x) into g(x)
1. Use the above applet to complete the task then confirm the the function on the readout matches the functions; f(x) and g(x), then sketch the two graphs.
2. Describe the transformation necessary to transform the graph f(x)( solid line) into g(x) (dashed line).
