Using graphical calculator to check graphs and investigate transformations
How to draw graphs onto the same axes
Select Graph from the main menu
For question 5, type in the function and using the X,θ,Tkey for x. Press EXE after each and DRAW (F6).
The axes may not fit the data well. You may not see all features of the graph.
Zoom (F2) gives several options – zoom out to make sure you can see all overall shape. Select OUT (F4) and press EXE to achieve this.
You can select the part of the graph you wish to examine more closely using Zoom BOX (F1). Draw the box by moving the cursor to one corner, press EXE then scroll it to the diagonally opposite corner. This allows the zoom to work differently in the horizontal and vertical directions.
Taking it further – using G-Solv to find the points of intersection
G-Solv (F6) enables you to find the key features of the graphs and INTSECT (F5) gives the co-ordinates of the points of intersection. Scrolling across gives the other points
Using MODIFY to investigate the constant of proportionality
In question 6, y is given as proportional to so the equation is of the form where k is the constant of proportionality. Type this equation into graph mode using the X,θ,T key for xand ALPHA K for k. Press MODIFY (F5). The calculator uses the previous value for k, which may be zero. A new value can be used by typing the value, or scrolling sideways – the step size can be altered by scrolling down, changing the step and returning to k once more.
Change the value of k can be changed so that the point (0.5, 1) lies on the graph.
If the scales are not correct, EXE returns to DRAW where Zoom (F2) and V-Window (F4) can be used to adjust the axes.
This trial and improvement method of finding k can be slow, so an algebraic method is often better, with this as a useful check.
Once the graph is correct, EXE returns to DRAW where functions such as Trace can be used to find the y value for other values of x.
Taking it further - using the function notation to investigate transformations
Transformations of any graph can be investigated by typing the function for the graph to be transformed as Y1. (You can later change this and see the effect of the same algebraic changes on different graphs)
Translation in the y direction
To investigate translations of , type into graph mode using the X,θ,T key for x. Type using ALPHA C for Cand Y using F1. (Scroll sideways so the cursor is in the box and the Y option will appear at the bottom of the screen.) Press EXE and MODIFY (F5) so that the value of C can be changed.
Stretch in y direction
To investigate stretches of , type into graph mode using the X,θ,T key for x. Type using ALPHA K for Kand Y using F1. Press EXE and MODIFY (F5) so that the value of K can be changed.
The calculator will use the previously used value for K (which may be zero) and can be changed by typing a new value, or scrolling sideways to a new value. Press EXIT to return to DRAW if the axes need to be adjusted in Zoom or V-Window.
To show the stretch works independently of the function itself, return to the table from DRAW by pressing G↔T (F6) and changing Y1 to another function.
Taking it further - using the function notation to investigate transformations requiring a change in the argument of the function
Translation in the x direction
The graph can be transformed to by putting using the X,θ,T key for x and typing . Scroll sideways to put the cursor in the box and the option to use F1 for Y will appear
EXE and MODIFY (F5) will draw the two graphs and the value of A can by altered by typing a new value or scrolling sideways.
Stretch in x direction
The graph can be transformed to by putting using the X,θ,T key for x and typing . Scroll sideways to put the cursor in the box and the option to use F1 for Y will appear
The sideways stretch is clearer when the applied to a different graph – this can be changed by pressing EXIT and G↔T and changing Y1, leaving Y2 unchanged.