[b][size=150]The absolute value function is [color=#ff0000]y = |x|[/color] , denoted by function g. [br][br][/size][/b]The transformed basic function is [color=#ff0000][b]y = a|bx - h| +k[/b][/color].[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][b][color=#ff00ff]Note: You can zoom in or out with the mouse.[/color][/b]

[b][size=150]Perform the following absolute value function transformation:[br][/size][/b][br][b]Vertical shift of 3 units up. [br][br][/b] The new function is [b][color=#ff0000]y=[/color][/b][b][color=#ff0000]|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 up.[br][/color][br][b][color=#ff00ff] Observe the transformation of the absolute value function.[/color][/b]

[b][size=150]Perform the following absolute value 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]|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]absolute value [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following absolute value 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]|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]absolute value [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following absolute value 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]|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][b][color=#ff00ff]absolute value [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following absolute value 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]|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][b][color=#ff00ff]absolute value [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following absolute value function transformation:[br][/size][/b][br][b]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]|x-3|[/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=3 which represents the horizontal shift of 3 units to the right. [br] Set k=3 which represents the vertical shift of 3 units up.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]absolute value [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following absolute value 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 =|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 represents the vertical shift of 3 units down.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]absolute value [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following absolute value 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 = |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 represents the vertical shift of 3 units down.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]absolute value [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following absolute value function transformation:[br][/size][/b][br][b]Vertical stretch by a factor of 3.[br][br][/b] New function: [color=#ff0000] [b]y = 3|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]absolute value [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following absolute value 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 = |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 represents[/color] [color=#0000ff]the vertical shift of 3 units up.[br][/color][br][color=#ff00ff][b] Observe the transformation of the absolute value function.[/b][/color]

[b][size=150]Perform the following absolute value 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| x|[/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=1/3.[br] Set b=1.[br] Set h= - 3 which represents the horizontal shift of 3 units to the left. [br] Set k= 3 which represents the vertical shift of 3 units up.[br][br][/color][color=#ff00ff][b] Observe the transformation of the [/b][/color][b][color=#ff00ff]absolute value [/color][/b][color=#ff00ff][b]function.[/b][/color]

[b][size=150]Perform the following absolute value function transformation:[br][/size][/b][br][b]Horizontal stretch by a factor of 1/3.[br][br][/b] New function: [color=#ff0000][b]y = |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]absolute value [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following absolute value function transformation:[br][/size][/b][br][b]Horizontal shrink by a factor of 3.[br][br][/b] New function: [b][color=#ff0000]y = |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]absolute value [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following absolute value function transformation:[br][/size][/b][br][b]Vertical shift of 3 units, a 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|x + 3| + 3[/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=1. Set b=1.[/color][color=#0000ff][br] Set h= - 3 which represents the horizontal shift of 3 units to the left. [br] Set k= 3 which represents the vertical shift of 3 units up.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]absolute value [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following absolute value function transformation:[br][/size][/b][br][b]Vertical shift of 3 units, a horizontal shift of 3 units to the left[br] and a vertical shrink by a factor of 1/2. [br][/b] [br] New function: [b][color=#ff0000]y = 1/2|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 represents the vertical shift of 3 units up.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]absolute value [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following absolute value function transformation:[br][/size][/b][br][b]Reflection over the x-axis. [br][br][/b] New function: [b][color=#ff0000]y = - |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]absolute value [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following absolute value function transformation:[br][/size][/b][br][b]Reflection over the y-axis. [br][br][/b] New function: [b] [color=#ff0000]y = |-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]absolute value [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following absolute value function transformation:[br][/size][/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]

[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]