# How to Graph Transformation on the TI-Nspire

Several types of functions have graphs that can be directly manipulated on the TI-Nspire screen. To accomplish this task, simply press [CTRL][CLICK to grab the graph and then use the Touchpad keys to perform a transformation.

As an example, create the graph of *y* = *x*^{2}. Two different options are possible:

**Perform a translation. Position the cursor on the vertex of the graph until the crossed, double-headed arrow symbol appears, and press [CTRL][CLICK] to grab the graph. Use the Touchpad keys to translate the graph and press [ESC] when finished.**Notice that the equation of the graph is updated automatically, in real time, as you move the graph, as shown in the first screen.

**Perform a stretch. Position the cursor on a side of the parabola until the****symbol appears and press [CTRL][CLICK] to grab the graph. Use the Touchpad keys to stretch the graph and press [ESC] when complete.**Notice that the equation of the graph, specifically the value

*a*in front of the parentheses, is automatically updated, as shown in the second screen.

Here is a list of the different functions that can be transformed using the same procedures just described:

Linear functions of the form

*y*=*b*, where*b*is a constantLinear functions of the form

*y*=*ax*+*b*, where*a*and*b*are constantsQuadratic functions of the form

*y*=*ax*^{2}+*bx*+*c*, where*a*,*b*, and*c*are constants or the form*y*=*a*(*x*–*h*)^{2}+*k*Exponential functions of the form

*y*=*e*^{ax}^{ + }^{b}^{ }+*c*, where*a*,*b*, and*c*are constantsExponential functions of the form

*y*=*be*^{ax}^{ }+*c*, where*a*,*b*, and*c*are constantsExponential functions of the form

*y*=*de*^{ax }^{+ }^{b}^{ }+*c*, where*a*,*b*,*c*, and*d*are constantsLogarithmic functions of the form

*y*=*a*ln(*cx*+*b*) +*d*, where*a*,*b*,*c*, and*d*are constantsSinusoidal functions of the form

*y*=*a*sin(*cx*+*b*) +*d*, where*a*,*b*,*c*, and*d*are constantsCosinusoidal functions of the form

*y*=*a*cos(*cx*+*b*) +*d*, where*a*,*b*,*c*, and*d*are constants

All the previously mentioned functions can be translated and stretched. However, in the case of the first two linear functions, the stretch looks more like a rotation about the *y*-intercept.

With a bit of practice, you will quickly learn where to find the positions on the graph where the translation and stretch symbols appear. For example, translate the graph of *a *sin(*cx* + *b*) + *d* by positioning the cursor at a point halfway between the maximum and minimum values. Any other point on the graph, TI-Nspire allows you to stretch the graph.