The rational or reciprocal function is y = 1/x , denoted by function g. The transformed basic function is y = 1/(x - h) + k Note: The 'slider' feature on the x-y coordinate plane can be used to change the h, and k values for the following exercises. To do so, place the cursor and hold it on the dot of the slider and slide it to the desired m and b values. To move the slider to a different location on the x-y plane, place the cursor and hold it on the line of the slider and move it to the desired location. Note: You can zoom in or out with the mouse.

Perform the following rational function transformation: Vertical shift of 3 units up. The new function is y=1/x +3 , denoted by function f. Set h=0 since there is no horizontal shift Set k=3 which represents the vertical shift of 3 units up. Observe the transformation of the rational function.

Perform the following rational function transformation: Vertical shift of 3 units down. The new function is y=1/x - 3 , denoted by function f. Set h=0 since there is no horizontal shift Set k= - 3 which represents the vertical shift of 3 units down. Observe the transformation of the rational function.

Perform the following rational function transformation: Horizontal shift of 3 units to the right. The new function i y=1/(x - 3) , denoted by function f. Set h=3 which represents the horizontal shift of 3 units to the right. Set k=0 since there is not vertical shift. Observe the transformation of the rational function.

Perform the following rational function transformation: Horizontal shift of 3 units to the left. The new function is y=1/(x+3) , denoted by function f. Set h=- 3 which represents the horizontal shift of 3 units to the left. Set k=0 since there is not vertical shift. Observe the transformation of the rational function.

Perform the following rational function transformation: Vertical shift of 3 units up plus a horizontal shift of 3 units to the right. New function: y = 1/(x-3) +3 , denoted by function f. Set h=3 which represents the horizontal shift of 3 units to the right. Set k=3 which represents the vertical shift of 3 units up. Observe the transformation of the rational function.

Perform the following rational function transformation: Vertical shift of 3 units down plus a horizontal shift of 3 units to the left. New function: y = 1/(x+3) - 3 , denoted by function f. Set h=- 3 which represents the horizontal shift of 3 units to the left. Set k=- 3 which represents the vertical shift of 3 units down. Observe the transformation of the rational function.

Perform the following rational function transformation: Vertical shift of 3 units down plus a horizontal shift of 3 units to the right. New function: y = 1/(x - 3) - 3, denoted by function f. Set h= 3 which represents the horizontal shift of 3 units to the right. Set k=- 3 which represents the vertical shift of 3 units down. Observe the transformation of the rational function.

Perform the following rational function transformation: Vertical shift of 3 units up plus a horizontal shift of 3 units to the left. New function: y = 1/(x+3) + 3, denoted by function f. Set h= - 3 which represents the horizontal shift of 3 units to the left. Set k= 3 which represents the vertical shift of 3 units up. Observe the transformation of the rational function.

Perform the following rational function transformation: Reflection over the x-axis. New function: y = - 1/x , denoted by function f. Place a negative in front of the entire equation. Set h= 0 since there is no horizontal shift. Set k= 0 since there is no vertical shift. Observe the transformation of the rational function.

Perform the following rational function transformation: Reflection over the y-axis. New function: y = 1/(-x ) , denoted by function f. Place a negative in front of the variable x. Set h= 0 since there is no horizontal shift. Set k= 0 since there is no vertical shift. Observe the transformation of the rational function.

Repeat this exercise as many times as desired until concept is mastered. Use different values of h and k.