Exploring Graphs of Absolute Value Functions in Sketchpad Name: _____________________________________ Start Up Directions: 1.) Graph | Define New Coordinate System 2.) Go to the Mac HD. Open the Applications Folder. Open the Sketchpad Folder. Open the Samples Folder. Open the Custom Tools folder. Open the Sliders File. (This will add the sliders tool to Sketchpad). Minimize the Sliders File. 3.) Click at the bottom of the Toolbar. Select Sliders. Select Basic Horizontal Sliders. 4.) In the GSP document. Click and move the mouse three times to create three sliders. Hit the esc key at the top left of the Mac to exit this mode. 5.) Click on the Toolbar. • Click on the second “a= ____” at the top. Choose the Label Tab. Change the label to h. Click on the “a” that corresponds to the second slider. Change the label to h. • Click on the third “a= ____” at the top. Choose the Label Tab. Change the label to k. Click on the “a” that corresponds to the third slider. Change the label to k. 6.) Graph | Plot new Function. Click the parameters in the sketch to enter them (a=, h = , k = ). Enter a*abs(x-h)+k. Note: To adjust the sliders, select the green dot on the slider. Adjust the sliders to that a = 1, h = 0 and k = 0. Write the equation of the graph. ____________________________ (This is the parent function for the family of absolute value functions) Fill out the table of values that corresponds with the function. x -2 -1 0 f(x) 1 Plot the parent function on the graph in red. Adjust the sliders so that a = 1, h = 3, and k = -4. Where is the vertex of the new graph? _____________________________ Write the new equation of the graph ______________________________ Describe the translation of the parent function to attain the new graph_____________ _______________________________________________________ 2 Exploring Graphs of Absolute Value Functions in Sketchpad Adjust the sliders so that a = 5, h = 3, and k = -4. Where is the vertex of the new graph? _____________________________ Write the equation of the new graph ______________________________ Slope: ________ Describe the translation of the parent function to attain the new graph_____________ _______________________________________________________ Adjust the sliders so that a = -5, h = 3, and k = -4. Where is the vertex of the new graph? _____________________________ Write the equation of the new graph ______________________________ Slope: ________ Describe the translation of the parent function to attain the new graph_____________ _______________________________________________________ Adjust the sliders so that a = 3, h = -5, and k = 2. Where is the vertex of the new graph? _____________________________ Write the equation of the new graph ______________________________ Slope: ________ Describe the translation of the parent function to attain the new graph_____________ _______________________________________________________ Adjust the sliders so that a = 1 , h = -2, and k = -5. 4 Where is the vertex of the new graph? _____________________________ Write the equation of the new graph ______________________________ Slope: ________ Describe the translation of the parent function to attain the new graph_____________ _______________________________________________________ Adjust the sliders so that a = 1 − , h = -1, and k = 4. 2 Where is the vertex of the new graph? _____________________________ Write the equation of the new graph ______________________________ Slope:_________ Describe the translation of the parent function to attain the new graph_____________ _______________________________________________________ Exploring Graphs of Absolute Value Functions in Sketchpad Select the green dot on the slider that corresponds with parameter a. Describe the two things that happen to the graph as you change parameter a. 1.)________________________________________________________________ 2.) _________________________________________________________________ What special property does the graph have when a = 0 ? _________________________ Select the green dot on the slider that corresponds with parameter h. What happens to the graph as you change the parameter h? ______________________ _____________________________________________________________________ What special property does the graph have when h = 0? ? ______________________ _____________________________________________________________________ Select the green dot on the slider that corresponds with parameter k. What happens to the graph as you change the parameter k? ______________________ _____________________________________________________________________ What special property does the graph have when k = 0 ? ______________________ _____________________________________________________________________