Can move the blue graph, [math]f_2\left(x\right)=log_2\left(x\right)[/math] onto the green graph of [math]f_3[/math] by a series of transformations? The blue graph is the function [math]f_2\left(x\right)=a\cdot log_b\left(n\left(x-h\right)\right)+k[/math]. Slider [i]a[/i] dilates in the [i]y[/i]-direction and if negative, reflects in the [i]x[/i]-axis. When Slider [i]n[/i] is -1, the graph is reflected about the [i]y[/i]-axis. Slider [i]b[/i] changes the base of the log function, which dilates in the [i]x[/i]-direction. Slider [i]h[/i] translates horizontally. Slider [i]k[/i] translates vertically. The graph of [math]f_1\left(x\right)=log_2\left(x\right)[/math] is shown dotted for reference.[br]A possible approach:[br][list=1][*]Adjust Slider [i]b[/i] to determine how the base is related to the distance between the asymptote and the point B[sub]2[/sub]? Determine the base, [i]b[/i], of the green graph ([math]f_3\left(x\right)[/math]).[/*][*]Do you need to reflect in the [i]x[/i]-axis? The direction of the asymptote (up or down) will help. Set Slider [i]a[/i] to -1 to reflect.[/*][*] Do you need to reflect in the [i]y[/i]-axis? The relative positions of points A and B will help. Set Slider [i]n[/i] to -1 to reflect.[/*][*]Move the graph horizontally with Slider [i]h[/i] and vertically with Slider [i]k[/i], to put Point A[sub]2[/sub] onto Point A[sub]3[/sub].[/*][*]Adjust Slider [i]a[/i] to dilate Point B[sub]2[/sub] onto Point B[sub]3[/sub].[size=100][size=85][br][/size][/size][/*][/list]To generate a new function [math]f_3\left(x\right)[/math], hit the refresh button in the top right corner.