[b][size=150]The logarithmic function is [color=#ff0000]y = log[sub]a[/sub]x[/color] , denoted by function g. [br][br][/size][/b]The transformed basic function is [b][size=150][color=#ff0000]y = b log[sub]a[/sub](x - h)[/color][/size][/b][b][color=#ff0000] +k where a > 1.[/color][/b][br][b][color=#ff0000][size=150][br]Note[/size][/color][/b]: The 'slider' feature on the x-y coordinate plane can be used to change the [color=#ff0000][b]a, b, h, and k[/b][/color] values [br] for the following exercises. To do so, place the cursor and hold it on the dot of the slider and [br] slide it to the desired m and b values.[br] To move the slider to a different location on the x-y plane, place the cursor and hold it on the line [br] of the slider and move it to the desired location.[br][br][b][color=#ff00ff]Note: You can zoom in or out with the mouse.[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][b]Vertical shift of 3 units up. Assume a = 2. [br][br][/b] The new function is [b][color=#ff0000]y=[/color][/b][b][size=150][color=#ff0000]log[sub]2[/sub]x[/color][/size][/b][b][color=#ff0000] +3[/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set b=1.[br] Set h=0 since there is no horizontal shift [br] Set k=3 which represents the vertical shift of 3 units up.[br][/color][br][b][color=#ff00ff] Observe the transformation of the logarithmic function.[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][b]Vertical shift of 3 units down. Assume a = 2.[br][br][/b] The new function is [b][color=#ff0000]y=[/color][/b][b][size=150][color=#ff0000]log[sub]2[/sub]x[/color][/size][/b][b][color=#ff0000] - 3[/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set b=1.[br] Set h=0 since there is no horizontal shift [br] Set k= - 3 which represents the vertical shift of 3 units down.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]logarithmic function.[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][b]Horizontal shift of 3 units to the right. Assume a=2.[br][br][/b] The new function is [b][color=#ff0000]y=[/color][/b][b][size=150][color=#ff0000]log[sub]2([/sub]x[/color][/size][/b][b][color=#ff0000] - 3)[/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set b=1.[br] Set h=3 which represents the horizontal shift of 3 units to the right. [br] Set k=0 since there is not vertical shift.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]logarithmic function.[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][b]Horizontal shift of 3 units to the left. Asume a=2.[br][br][/b] The new function is [b][color=#ff0000]y=[/color][/b][b][size=150][color=#ff0000]log[sub]2([/sub]x[/color][/size][/b][b][color=#ff0000] + 3)[/color][/b], denoted by function f.[br][br] [color=#0000ff]Set b=1.[br] Set h=- 3 which represents the horizontal shift of 3 units to the left. [br] Set k=0 since there is not vertical shift.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]logarithmic function.[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][b]Vertical shift of 3 units up plus a horizontal shift of 3 units to the right. Assume a = 2.[br][br][/b] New function: [b][color=#ff0000]y = [/color][/b][b][size=150][color=#ff0000]log[sub]2([/sub]x[/color][/size][/b][b][color=#ff0000] - 3)[/color][/b][b][color=#ff0000] + 3[/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set b=1.[br] Set h=3 which represents the horizontal shift of 3 units to the right. [br] Set k=3 which [/color]represents [color=#0000ff]the vertical shift of 3 units up.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]logarithmic function.[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][b]Vertical shift of 3 units down plus a horizontal shift of 3 units to the left. Assume a= 2.[br][br][/b] New function: [b][color=#ff0000]y = [/color][/b][b][size=150][color=#ff0000]log[sub]2[/sub](x[/color][/size][/b][b][color=#ff0000] + 3)[/color][/b][b][color=#ff0000] - 3[/color][/b], denoted by function f.[br][br] [color=#0000ff]Set b=1.[br] Set h=- 3 which represents the horizontal shift of 3 units to the left. [br] Set k=- 3 which [/color]represents [color=#0000ff]the vertical shift of 3 units down.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]logarithmic function.[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][b]Vertical shift of 3 units down plus a horizontal shift of 3 units to the right. Assume a=2.[br][br][/b] New function: [b][color=#ff0000]y = [/color][/b][b][size=150][color=#ff0000]log[sub]2[/sub](x[/color][/size][/b][b][color=#ff0000] - 3)[/color][/b][b][color=#ff0000] - 3[/color][/b], denoted by function f.[br][br] [color=#0000ff]Set b=1.[br] Set h= 3 which represents the horizontal shift of 3 units to the right. [br] Set k=- 3 which [/color]represents [color=#0000ff]the vertical shift of 3 units down.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]logarithmic function.[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][b]Vertical shift of 3 units up plus a horizontal shift of 3 units to the left. Assume a =2.[br][br][/b] New function: [b][color=#ff0000]y = [/color][/b][b][size=150][color=#ff0000]log[sub]2[/sub](x[/color][/size][/b][b][color=#ff0000] + 3)[/color][/b][b][color=#ff0000] + 3[/color][/b], denoted by function f.[br][br] [color=#0000ff]Set b=1.[br] Set h= - 3 which represents the horizontal shift of 3 units to the left. [br] Set k= 3 which [/color]represents [color=#0000ff]the vertical shift of 3 units up.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]logarithmic function.[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][b]Vertical stretch by a factor of 3. [/b] [b]Assume a =2.[br][/b][br] New function: [color=#ff0000] [b]y = 3 lo[/b][/color][b][size=150][color=#ff0000]g[sub]2[/sub]x[/color][/size][/b] , denoted by function f.[br][br] [color=#0000ff]Set b=1.[br] Set h= 0 since there is no horizontal shift.[br] Set k= 0 since there is no vertical shift.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]logarithmic function.[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][b]Vertical shrink by a factor of 1/3. [/b][b]Assume a =2.[/b] [br][br] New function: [b][color=#ff0000]y = 1/3 [/color][/b][color=#ff0000][b] lo[/b][/color][b][size=150][color=#ff0000]g[sub]2[/sub]x[/color][/size][/b] , denoted by function f.[br][br] [color=#0000ff]Set b=1.[br] Set h= - 3 which represents the horizontal shift of 3 units to the left. [br] Set k= 3 which [/color]represents [color=#0000ff]the vertical shift of 3 units up.[br][br][/color][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]logarithmic function.[/color][/b][b][color=#ff00ff].[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][b]Vertical shift of 3 units up, horizontal shift of 3 units to the left [br] and a vertical stretch by a factor of 2 . [/b][b]Assume a =2.[/b] [br][br] New function: [b][color=#ff0000]y = 2[/color][/b][color=#ff0000][b] lo[/b][/color][b][size=150][color=#ff0000]g[sub]2[/sub](x + 3 ) + 3[/color][/size][/b], denoted by function f.[br][br] [color=#0000ff]Set b=1.[br] Set h= - 3 which represents the horizontal shift of 3 units to the left. [br] Set k= 3 which [/color]represents [color=#0000ff]the vertical shift of 3 units up.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]logarithmic function.[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][b]Vertical shift of 3 units up, horizontal shift of 3 units to the left, [br] a vertical shrink by a factor of 1/2 . [/b][b]Assume a =2.[/b] [br] [br] New function: [b][color=#ff0000]y = 1/[/color][/b][b][color=#ff0000]2[/color][/b][color=#ff0000][b] lo[/b][/color][b][size=150][color=#ff0000]g[sub]2[/sub](x + 3 ) + 3[/color][/size][/b], denoted by function f.[br][br] [color=#0000ff]Set b=1.[br] Set h= - 3 which represents the horizontal shift of 3 units to the left. [br] Set k= 3 which [/color]represents [color=#0000ff]the vertical shift of 3 units up.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]logarithmic function.[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][b]Horizontal stretch by a factor of 1/3. [/b][b]Assume a =2.[/b] [br][br] New function: [color=#ff0000][b]y = [/b][/color][color=#ff0000][b]lo[/b][/color][b][size=150][color=#ff0000]g[sub]2[/sub]((1/3)x)[/color][/size][/b] , denoted by function f.[br][br][color=#0000ff] Place a 1/3 in front of the variable x.[br][/color][color=#0000ff] Set b=1.[br] Set h= 0 since there is no horizontal shift.[br] Set k= 0 since there is no vertical shift.[br][/color][br][color=#ff00ff][b] Observe the transformation of the [/b][/color][b][color=#ff00ff]logarithmic function.[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][b]Horizontal shrink by a factor of 3. [/b][b]Assume a =2.[/b] [br][br] New function: [b][color=#ff0000]y = [/color][/b][color=#ff0000][b] lo[/b][/color][b][size=150][color=#ff0000]g[sub]2[/sub](2x)[/color][/size][/b], denoted by function f.[br][br][color=#0000ff] Place a 2 in front of the variable x.[br][/color][color=#0000ff] Set b = 1.[br] Set h= 0 since there is no horizontal shift.[br] Set k= 0 since there is no vertical shift.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]logarithmic function.[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][br][b]Reflection over the x-axis. [/b][b]Assume a =2.[/b] [br][br] New function: [b][color=#ff0000]y = - [/color][/b][color=#ff0000][b]lo[/b][/color][b][size=150][color=#ff0000]g[sub]2[/sub]x[/color][/size][/b] , denoted by function f.[br][br] [color=#0000ff]Set b = - 1.[br] Set h= 0 since there is no horizontal shift.[br] Set k= 0 since there is no vertical shift.[br][br][/color][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]logarithmic function.[/color][/b]

[b][size=150]Perform the following logarithmic function transformation:[br][/size][/b][br][b]Reflection over the y-axis. [/b][b]Assume a =2.[/b] [br][br] New function: [b] [color=#ff0000]y = [/color][/b][color=#ff0000][b]lo[/b][/color][b][size=150][color=#ff0000]g[sub]2[/sub](-x)[/color][/size][/b], denoted by function f.[br][br][color=#0000ff] Place a negative in front of the variable x.[br] Set h= 0 since there is no horizontal shift.[br] Set k= 0 since there is no vertical shift.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]logarithmic function.[/color][/b]

[br][b]Repeat this exercise as many times as desired until concept is mastered. [br][br][/b] Use different values of [color=#ff0000][b]a, b, h and k[/b][/color].