Transformed Log Graph

A Challenge

Can move the blue graph, onto the green graph of by a series of transformations? The blue graph is the function . Slider a dilates in the y-direction and if negative, reflects in the x-axis. When Slider n is -1, the graph is reflected about the y-axis. Slider b changes the base of the log function, which dilates in the x-direction. Slider h translates horizontally. Slider k translates vertically. The graph of is shown dotted for reference. A possible approach:
  1. Adjust Slider b to determine how the base is related to the distance between the asymptote and the point B2? Determine the base, b, of the green graph ().
  2. Do you need to reflect in the x-axis? The direction of the asymptote (up or down) will help. Set Slider a to -1 to reflect.
  3.  Do you need to reflect in the y-axis? The relative positions of points A and B will help. Set Slider n to -1 to reflect.
  4. Move the graph horizontally with Slider h and vertically with Slider k, to put Point A2 onto Point A3.
  5. Adjust Slider a to dilate Point B2 onto Point B3.
To generate a new function , hit the refresh button in the top right corner.