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Online Tutorial -

CG50: How to Transform Graphs

CG50: How to Transform Graphs

In this tutorial, we're looking at how to use modify in graph mode to explore transformation of graphs. The graph I'm using will be y equals cosX. The calculator uses capital Y, much like the letter f in the standard function notation f of x. You can use any graph you like as y one and see how the transformation works on other graphs also. To work along with this tutorial, you'll find it easiest to reset the calculator before starting so your screen matches the one in the video.

With the default settings, the angle type is set in radians. So open graph mode and in Y1type the equation of the graph to be transformed, and press enter. For Y2 enter a constant using the alpha key than F1 for function y and enter 1 to show which function is being transformed. Use modify and scroll sideways to change the value of the constant.

Notice how the added constant translates the curve in the Y direction. If you were going to go back and change F1, you could see how the transformation of that new graph works without altering Y2 at all. For our next transformation, exit to graph mode and then exit graph mode to get back to your list of functions. Just edit Y2 by highlighting it and scrolling sideways. Go past the plus and delete it. And then A now becomes a multiplier. Enter and modify.

Notice the constant now stretches the graph in the Y direction. You can't adjust the axes while still in modifying, so to do so, exit graph mode and now zoom and view window will be active. To get transformations in the x direction, we will need to change the argument of the function. Press exit twice to get to the list of functions and then delete Y2.

If you now scroll sideways, then Y will appear at the bottom of the screen and you can type transformed equations using F1 to get Y, the variable key for X and Alpha B to type the B. And then when you're ready, enter the equation. Press modify and change the step size to Pi over six. Notice the fraction notation that the calculator uses in this mode. Now when you scroll back up to B, and then as you scroll sideways, you can change the value of B in steps of Pi over six. Notice the graph is translated in the X direction by B. Exit modify and then exit graph.

And now edit Y2 by highlighting it and scrolling sideways past the parts that need changing and delete. Scroll to put B in the correct place and then enter. Now modify. The previous value of B has been used. So choose integer values for B by typing them in, and then fractional values to see the effect of changing B. Notice the constant now stretches the graph in the x direction. Explore to find a link between the value of B and the scale factor of the stretch. To show there's nothing special about the graph of Y equals cosX, go back to your list of functions and change Y1 now into any of the type of graph and, even without changing Y2, you'll see the same stretch of your new graph.

You can find additional resources at education.casio.co.uk.