[size=150][b]The rational or reciprocal function is [color=#ff0000]y[/color][color=#ff0000] = 1/[/color][/b][/size][size=150][color=#ff0000][b]x[/b][/color][b] , denoted by function g.[br] [br][/b][/size]The transformed basic function is [color=#ff0000][b]y = 1/(x - h) + k[br][/b][/color][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]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 rational 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]1/x [/b][b][color=#ff0000] +3[/color][/b] , denoted by function f.[br][br] [color=#0000ff] 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 rational function.[/color][/b]

[b][size=150]Perform the following rational 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]1/x [/b][b][color=#ff0000] - 3[/color][/b] , denoted by function f.[br][br] [color=#0000ff] 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 rational function.[/color][/b]

[b][size=150]Perform the following rational function transformation:[br][/size][/b][br][b]Horizontal shift of 3 units to the right. [br][br][/b] The new function i [b][color=#ff0000]y=[/color][/b][b]1/(x - 3)[/b] , denoted by function f.[br][br][color=#0000ff] 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 rational function.[/color][/b]

[b][size=150]Perform the following rational 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=1/(x+3)[/color] [/b] , denoted by function f.[br][br][color=#0000ff] 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 rational function.[/color][/b]

[b][size=150]Perform the following rational 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][color=#ff0000]y = 1/(x-3) +3[/color][/b] , denoted by function f.[br][br][color=#0000ff] 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 rational function.[/color][/b]

[b][size=150]Perform the following rational 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 = 1/(x+3) - 3 [/color][/b], denoted by function f.[br][br][color=#0000ff] 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 rational function.[/color][/b]

[b][size=150]Perform the following rational 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 = 1/(x - 3) - 3[/color][/b], denoted by function f.[br][br][color=#0000ff] 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]rational [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following rational 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 = 1/(x+3) + 3[/color][/b], denoted by function f.[br][br][color=#0000ff] 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]rational [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following rational function transformation:[br][/size][/b][br][b]Reflection over the x-axis. [br][br][/b] New function: [b][color=#ff0000]y = - 1/x [/color][/b] , denoted by function f.[br][br][color=#0000ff] Place a negative in front of the entire equation.[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]rational [/color][/b][b][color=#ff00ff]function.[/color][/b]

[b][size=150]Perform the following rational function transformation:[br][/size][/b][br][b]Reflection over the y-axis. [br][br][/b] New function: [b] [color=#ff0000]y = 1/(-x )[/color][/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]rational [/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] h and k[/b][/color].