Translation and Stretching of Graphs
A Java Program Tutorial
This exercise gives you practice at looking at a graph that has been translated and stretched and then writing the equation for it. The basic form of the equation is written in the panel to the right of the applet and you're mission is to put the correct numbers into the text boxes so that the equation is exactly that of the function on the left that is graphed in blue. The function corresponding to the coefficients in the text boxes is drawn in red, so you control the graph of this function. When you enter coefficients into the text boxes and hit the enter key, the red function is redrawn. You're goal is to enter coefficients so that the red function completely covers the graph of the blue one. When you do that you won't be able to see the blue one. At that point, you're score is increased by one.
This requires that you be able to look at the blue function and figure out how it has been translated and stretched from the standard version of the function presented in section 4.5 of the text. You have an unlimited number of tries and hopefully incorrect tries will teach you a lot about translating and stretching functions. If one example is too difficult, simply hit the next button and try another example. However, you will not get a score for that example and there are only ten examples of each type. You will cycle through the examples and if you never match one, no score will be recorded. The score will be recorded after you match the tenth example, so make sure that you are consistently matching near the end or you won't get a score. You should not leave the page until a dialogue box comes up saying that you are done. If you want to work on that function some more or get a better score, simply reload the page.
Here is a brief description of the controls of the program. The right hand panel is the panel of controls, with two buttons at the top. The button on the right was supposed to take you to the next exercise but the required function is not supported by all browsers so it currently is disabled. The left hand button, which says "Next", is the one that works and simply takes you to the next example.
Below the buttons is an equation with text boxes where the numbers in the equation go. You type your own numbers into the text areas and when you hit the "enter" key a graph will be drawn in red on the axes on the left. There are slidebars beside the axes to adjust the view. The inner scrollbars stretch the graph and the outer ones slide the graph. However, they don't work on all browsers and so the examples are designed to not need them. The graph of the function you created drawn in red and there is a target function drawn in blue. Your goal is to type coefficients into your function so that its graph matches the one drawn in blue.
The first page lets you practice graphing the absolute value function. The second page works with graphs of parabolas and the third works with the cubic functions The fourth page involves graphs of the square root function and the fifth, the cube root function. Each page currently has ten examples. To start, click on the link below that says "Absolute Value Functions". The applets will navigate you to the next page automatically. Should your browser not implement the automatic navigation, click on the "Back" button until you get back to this page and use the links below to go to all of the pages. Otherwise, When you are navigated back to this page automatically, you are done with the entire assignment. Enjoy!