[b][size=150]The square root function is[color=#ff0000] y= SQRT X, [/color]denoted by function g. [br][br][/size][/b]The transformed basic function is [b][color=#ff0000]y = a SQRT(bx - h)[sup]2[/sup] +k[/color][/b][br][br][b][color=#ff0000][size=150]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][color=#ff00ff][b]Note: You can zoom in or out with the mouse.[/b][/color]

[b][size=150]Perform the following square root function transformation:[br][/size][/b][br][b]Vertical shift of 3 units up. [br][br][/b] The new function is [b][color=#ff0000]y=SQRT (x) +3[/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=1. 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 square root function.[/color][/b]

[b][size=150]Perform the following square root function transformation:[br][/size][/b][br][b]Vertical shift of 3 units down. [br][br][/b] The new function is [b][color=#ff0000]y=[/color][/b][b][color=#ff0000]SQRT (x)[/color][/b][b][color=#ff0000] - 3[/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=1. 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]square root [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following square root function transformation:[br][/size][/b][br][b]Horizontal shift of 3 units to the right. [br] [br][/b] The new function is [b][color=#ff0000]y=[/color][/b][b][color=#ff0000]SQRT (x -3)[/color][/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 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]square root [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following square root function transformation:[br][/size][/b][br][b]Horizontal shift of 3 units to the left. [br][br][/b] The new function is [b][color=#ff0000]y=[/color][/b][b][color=#ff0000]SQRT [/color][/b][b][color=#ff0000](x+3)[/color][/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][color=#ff00ff]square root [/color][/b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following square root function transformation:[br][/size][/b][b][br]Vertical shift of 3 units up plus a horizontal shift of 3 units to the right. [br][br][/b] New function: [b]y = [/b][b][color=#ff0000]SQRT [/color][/b][b][color=#ff0000](x-3) +3[/color][/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 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]square root [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following square root function transformation:[br][/size][/b][br][b]Vertical shift of 3 units down plus a horizontal shift of 3 units to the left. [br][br][/b] New function: [b][color=#ff0000]y = [/color][/b][b][color=#ff0000]SQRT [/color][/b][b][color=#ff0000](x+3) - 3[/color][/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=- 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]square root [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following square root function transformation:[br][/size][/b][br][b]Vertical shift of 3 units down plus a horizontal shift of 3 units to the right. [br][br][/b] New function: [b][color=#ff0000]y = [/color][/b][b][color=#ff0000]SQRT [/color][/b][b][color=#ff0000](x - 3) - 3[/color][/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 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]square root [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following square root function transformation:[br][/size][/b][br][b]Vertical shift of 3 units up plus a horizontal shift of 3 units to the left. [br][br][/b] New function: [b][color=#ff0000]y = [/color][/b][b][color=#ff0000]SQRT [/color][/b][b][color=#ff0000](x + 3) + 3[/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=1.[/color] [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]square root [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following square root function transformation:[br][/size][/b][br][b]Vertical stretch by a factor of 3.[br][br][/b] New function: [color=#ff0000] [b]y = 3 [/b][/color][b][color=#ff0000]SQRT ([/color][/b][color=#ff0000][b] x)[/b][/color], denoted by function f. [br][br] [color=#0000ff]Set a=3. 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]square root [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following square root function transformation:[br][/size][/b][br][b]Vertical shrink by a factor of 1/3.[br][br][/b] New function: [b][color=#ff0000]y = 1/3 [/color][/b][b][color=#ff0000]SQRT ([/color][/b][b][color=#ff0000]x)[/color][/b] , denoted by function f. [br][br] [color=#0000ff]Set a=1/3. 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][color=#ff00ff][b] Observe the transformation of the [/b][/color][b][color=#ff00ff]square root [/color][/b][color=#ff00ff][b]function.[/b][/color]

[b][size=150]Perform the following square root function transformation:[br][/size][/b][b][br]Horizontal stretch by a factor of 1/3.[br][br][/b] New function: [color=#ff0000][b]y = [/b][/color][b][color=#ff0000]SQRT [/color][/b][color=#ff0000][b](1/3x)[/b] [/color] , denoted by function f.[br][br] [color=#0000ff]Set a =1. Set b=1/3.[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]square root [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following square root function transformation:[br][/size][/b][br][b]Horizontal shrink by a factor of 3[br][br][/b] New function: [b][color=#ff0000]y = [/color][/b][b][color=#ff0000]SQRT [/color][/b][b][color=#ff0000](3x)[/color][/b] , denoted by function f. [br][br] [color=#0000ff]Set a =1. Set b=3.[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]square root [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following square root function transformation:[br][br][/size][/b][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. [br][br][/b] New function: [b][color=#ff0000]y = 2[/color][/b][b][color=#ff0000]SQRT [/color][/b][b][color=#ff0000](x + 3) + 3[/color][/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= 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]square root [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following square root 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 shrink by a factor of 1/2. [br][br][/b] New function: [b][color=#ff0000]y = 1/2[/color][/b][b][color=#ff0000]SQRT [/color][/b][b][color=#ff0000](x + 3) + 3[/color][/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= 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]square root [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following square root function transformation:[br][/size][/b][br][b]Reflection over the x-axis. [br][br][/b] New function: [b][color=#ff0000]y = - [/color][/b][b][color=#ff0000]SQRT (x)[/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=-1. 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]square root [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following square root function transformation:[br][/size][/b][br][b]Reflection over the y-axis. [br][br][/b] New function: [b] [color=#ff0000]y = [/color][/b][b][color=#ff0000]SQRT [/color][/b][b][color=#ff0000](-x)[/color][/b] , denoted by function f.[br][br] [color=#0000ff] Set a=1. 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]square root [/color][/b][b][color=#ff00ff]function.[/color][/b]

[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].