So far you have looked at the effects of h and k on functions of the form y − k = f(x) and y = f(x − h). Next you will look at combining these ideas to predict the effects of h and k on functions of the form y − k = f(x − h). Often this equation is rearranged to isolate y, giving y = f(x − h) + k. How do you think this function will respond to changing h and k?

 

Try This 3

 

Open Translations [y = f(x − h) + k].

 

 

Step 1: Select a cubic function using the button.

 

Step 2: Use the applet to complete a table like the one that follows. The equation of the graph is shown above the graph.

 

Function in Form y = f(x − h) + k	Value of h	Value of k	Effect on Graph	Diagram
y = x3
y = (x − 2)3 + 1
y = (x + 3)3 − 4

 

Step 3: Push the SET FCN button at the bottom right of the diagram and select the absolute-value function .

 

Step 4: Use this function to complete a table like the one that follows.

 

Function in Form y = f|x − h| + k	Value of h	Value of k	Effect on Graph	Diagram
y = |x|
y = |x + 2| + 3
y = |x − 2| − 4

1. What effects do h and k have on a function that contains both h and k?
2. How do the effects of changing h and k compare for the cubic function? The absolute-value function?

Save your responses in your course folder.