# 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 is shown dotted for reference.
A possible approach:
, hit the refresh button in the top right corner.

*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- Adjust Slider
*b*to determine how the base is related to the distance between the asymptote and the point B_{2}? 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 A_{2}onto Point A_{3}. - Adjust Slider
*a*to dilate Point B_{2}onto Point B_{3}.