[left][/left][right]سيوضح هذا التطبيق الصغير أساسيات الوظائف المتبادلة. سيغير شريط التمرير a بسط الخط.[br][/right] يقوم شريط التمرير h بتغيير الوضع الأفقي للمنحنى.[br] يقوم شريط التمرير k بتغيير الوضع الرأسي للمنحني.[br] يعكس شريط التمرير sy المنحنى عبر المحور y.[br] يعكس شريط تمرير sx المنحنى عبر المحور السيني.[img]data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxOCIgaGVpZ2h0PSIxOCIgdmlld0JveD0iMCAwIDI0IDI0Ij48cGF0aCBmaWxsPSJub25lIiBkPSJNMCAwaDI0djI0SDB6Ii8+PHBhdGggZD0iTTcgMTRINXY1aDV2LTJIN3YtM3ptLTItNGgyVjdoM1Y1SDV2NXptMTIgN2gtM3YyaDV2LTVoLTJ2M3pNMTQgNXYyaDN2M2gyVjVoLTV6Ii8+PC9zdmc+[/img]

Rational or Reciprocal Function Transformation Exercise[size=150]The rational or reciprocal function is [color=#ff0000]y[/color][color=#ff0000] = 1/[/color][/size][size=150][color=#ff0000]x[/color] , denoted by function g.[br] [br][/size]The transformed basic function is [color=#ff0000]y = 1/(x - h) + k[br][/color][color=#ff0000][size=150][br]Note[/size][/color]: The 'slider' feature on the x-y coordinate plane can be used to change the [color=#ff0000]h, and k[/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]Note: You can zoom in or out with the mouse.[/color]Exercise 1[size=150]Perform the following rational function transformation:[br][/size][br]Vertical shift of 3 units up. [br][br] The new function is [color=#ff0000]y=[/color]1/x [color=#ff0000] +3[/color] , 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][color=#ff00ff] Observe the transformation of the rational function.[/color]Exercise 2[size=150]Perform the following rational function transformation:[br][/size][br]Vertical shift of 3 units down. [br][br] The new function is [color=#ff0000]y=[/color]1/x [color=#ff0000] - 3[/color] , 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][color=#ff00ff] Observe the transformation of the rational function.[/color]Exercise 3[size=150]Perform the following rational function transformation:[br][/size][br]Horizontal shift of 3 units to the right. [br][br] The new function i [color=#ff0000]y=[/color]1/(x - 3) , 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][color=#ff00ff] Observe the transformation of the rational function.[/color]Exercise 4[size=150]Perform the following rational function transformation:[br][/size][br]Horizontal shift of 3 units to the left. [br][br] The new function is [color=#ff0000]y=1/(x+3)[/color] , 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][color=#ff00ff] Observe the transformation of the rational function.[/color]Exercise 5[size=150]Perform the following rational function transformation:[br][/size][br]Vertical shift of 3 units up plus a horizontal shift of 3 units to the right. [br][br] New function: [color=#ff0000]y = 1/(x-3) +3[/color] , 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][color=#ff00ff] Observe the transformation of the rational function.[/color]Exercise 6[size=150]Perform the following rational function transformation:[br][/size][br]Vertical shift of 3 units down plus a horizontal shift of 3 units to the left. [br][br] New function: [color=#ff0000]y = 1/(x+3) - 3 [/color], 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][color=#ff00ff] Observe the transformation of the rational function.[/color]Exercise 7[size=150]Perform the following rational function transformation:[br][/size][br]Vertical shift of 3 units down plus a horizontal shift of 3 units to the right. [br][br] New function: [color=#ff0000]y = 1/(x - 3) - 3[/color], 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][color=#ff00ff] Observe the transformation of the [/color][color=#ff00ff]rational [/color][color=#ff00ff]function.[/color]Exercise 8[size=150]Perform the following rational function transformation:[br][/size][br]Vertical shift of 3 units up plus a horizontal shift of 3 units to the left. [br][br] New function: [color=#ff0000]y = 1/(x+3) + 3[/color], 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][color=#ff00ff] Observe the transformation of the [/color][color=#ff00ff]rational [/color][color=#ff00ff]function.[/color]Exercise 9[size=150]Perform the following rational function transformation:[br][/size][br]Reflection over the x-axis. [br][br] New function: [color=#ff0000]y = - 1/x [/color] , 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][color=#ff00ff] Observe the transformation of the [/color][color=#ff00ff]rational [/color][color=#ff00ff]function.[/color]Exercise 10[size=150]Perform the following rational function transformation:[br][/size][br]Reflection over the y-axis. [br][br] New function: [color=#ff0000]y = 1/(-x )[/color] , 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][color=#ff00ff] Observe the transformation of the [/color][color=#ff00ff]rational [/color][color=#ff00ff]function.[/color]Exercise 11Repeat this exercise as many times as desired until concept is mastered. [br][br] Use different values of [color=#ff0000] h and k[/color]