Transformed Log Graph
- Author:
- Raymond Summit
- Topic:
- Logarithm, Logarithmic Functions
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:
- 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 ().
- 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.
- 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.
- Move the graph horizontally with Slider h and vertically with Slider k, to put Point A2 onto Point A3.
- Adjust Slider a to dilate Point B2 onto Point B3.