[b][size=150]The exponential function is [color=#ff0000]y = a[/color][/size][/b][b][size=150][color=#ff0000][sup]x[/sup][/color] , denoted by function g. [br] [/size][/b][b][size=150][color=#ff0000][math]\cdot[/math][/color][/size][/b][br]The transformed basic function is [b][size=150][color=#ff0000]y = b a[/color][/size][/b][b][size=150][color=#ff0000][sup]x+h[/sup][/color] [color=#ff0000]+ k with [/color][/size][size=150][color=#ff0000]a > 0, a [/color][color=#ff0000]≠ [/color][color=#ff0000]1[/color][/size][size=150][color=#ff0000].[/color][/size][/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 exponential 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=2[/color][/b][b][size=150][color=#ff0000][sup]x[/sup][/color][/size][/b][b][color=#ff0000] +3[/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=2. 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 exponential function.[/color][/b]

[b][size=150]Perform the following exponential function transformation:[br][/size][/b][br][b]Vertical shift of 3 units down. [/b][b]Assume a=2.[/b] [br][br] The new function is [b][color=#ff0000]y=[/color][/b][b][color=#ff0000]2[/color][/b][b][size=150][color=#ff0000][sup]x[/sup][/color][/size][/b][b][color=#ff0000] - 3[/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=2. 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]exponential [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following exponential function transformation:[br][/size][/b][br][b]Horizontal shift of 3 units to the right. [/b][b]Assume a=2.[/b] [br][br] The new function is [b][color=#ff0000]y=[/color][/b][b][color=#ff0000]2[/color][/b][b][size=150][color=#ff0000][sup]x - 3[/sup][/color][/size][/b], denoted by function f.[br][br] [color=#0000ff]Set a=2. 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]exponential [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following exponential function transformation:[br][/size][/b][br][b]Horizontal shift of 3 units to the left. [/b][b]Assume a=2.[/b] [br][br] The new function is [b][color=#ff0000]y=[/color][/b][b][color=#ff0000]2[/color][/b][b][size=150][color=#ff0000][sup]x + 3[/sup][/color][/size][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=1. 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]exponential [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following exponential function transformation:[br][/size][/b][br][b]Vertical shift of 3 units up plus a horizontal shift of 3 units to the right. [/b][b]Assume a=2.[/b] [br][br] New function: [b][color=#ff0000]y =[/color] [/b][b][color=#ff0000]2[/color][/b][b][size=150][color=#ff0000][sup]x - 3[/sup][/color][/size][/b][b][color=#ff0000] + 3 [/color][/b], denoted by function f.[br][br] [color=#0000ff]Set a=2. 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]exponential [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following exponential function transformation:[br][/size][/b][br][b]Vertical shift of 3 units down plus a horizontal shift of 3 units to the left. [/b][b]Assume a=2.[/b] [br][br] New function: [b][color=#ff0000]y = [/color][/b][b][color=#ff0000]y =[/color] [/b][b][color=#ff0000]2[/color][/b][b][size=150][color=#ff0000][sup]x + 3[/sup][/color][/size][/b][b][color=#ff0000] - 3[/color][/b], denoted by function f.[br][br] [color=#0000ff]Set a=2. 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]exponential [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following exponential function transformation:[br][/size][/b][br][b]Vertical shift of 3 units down plus a horizontal shift of 3 units to the right. [/b][b]Assume a=2.[/b] [br][br] New function: [b][color=#ff0000]y = [/color][/b][b][color=#ff0000]2[/color][/b][b][size=150][color=#ff0000][sup]x - 3[/sup][/color][/size][/b][b][color=#ff0000] - 3 [/color][/b], denoted by function f.[br][br] [color=#0000ff]Set a=2. 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]exponential [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following exponential function transformation:[br][/size][/b][br][b]Vertical shift of 3 units up plus a horizontal shift of 3 units to the left. [/b][b]Assume a=2.[/b] [br][br] New function: [b][color=#ff0000]y = [/color][/b][b][color=#ff0000]2[/color][/b][b][size=150][color=#ff0000][sup]x + 3[/sup][/color][/size][/b][b][color=#ff0000] + 3[/color][/b], denoted by function f.[br][br] [color=#0000ff]Set a=2. 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]exponential [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following exponential function transformation:[br][/size][/b][br][b]Vertical stretch by a factor of 3. [/b][b]Assume a=2.[/b] [br][br] New function: [color=#ff0000] [b]y = 3* [/b][/color][b][color=#ff0000]2[/color][/b][b][size=150][color=#ff0000][sup]x[/sup][/color][/size][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=2. Set b=3. 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]exponential [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following exponential 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][b][color=#ff0000]2[/color][/b][b][size=150][color=#ff0000][sup]x[/sup][/color][/size][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=2. Set b=1/3.[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]exponential [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following exponential 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 4 . [/b][b]Assume a=2.[/b] [br][br] New function: [b][color=#ff0000]y = [/color][/b][b][color=#ff0000] 4*[/color][/b][b][color=#ff0000]2[/color][/b][b][size=150][color=#ff0000][sup]x+3 [/sup][/color][/size][/b][b][color=#ff0000]+ 3 [/color][/b], denoted by function f.[br][br] [color=#0000ff]Set a=2. Set b=4.[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]exponential [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following exponential 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 . Assume a =2.[br][br][/b] New function: [b][color=#ff0000]y = (1/2)[/color][/b][b][color=#ff0000]*[/color][/b][b][color=#ff0000]2[/color][/b][b][size=150][color=#ff0000][sup]x+3 [/sup][/color][/size][/b][b][color=#ff0000]+ 3[/color][/b], denoted by function f.[br][br] [color=#0000ff]Set a=2. Set b=1/2.[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]exponential [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following exponential function transformation:[br][/size][/b][br][b]Reflection over the x-axis. [/b][b]Assume a=2.[/b] [br][br] New function: [b][color=#ff0000]y = - [/color][/b][b][color=#ff0000]2[/color][/b][b][size=150][color=#ff0000][sup]x[/sup][/color][/size][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=2. 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]exponential [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following exponential 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][b][color=#ff0000]2[/color][/b][b][size=150][color=#ff0000][sup]-x [/sup][/color][/size][/b], denoted by function f.[br][br] [color=#0000ff] Set a = 2. 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]exponential [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][br]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].[br] Try using [b][color=#ff0000]0 < a < 1.[/color][/b]