Transformations

Subject Areas

Tools / Misc

bCalc

drag-N-drop

scrnGC3: f(x) Plot Input

scrnGC4: g(x) Plot Input

The inputs above will be hidden when the program finally gets launched. Currently, I am not hiding them even when you close the calculator. The purpose of the inputs is to help in debugging. This allows you to enter simple code on the calculator screen but the program translates the input to javascript math. Give it a try and see if you notice any obvious problems or have suggestions for improvements.

gCalc

drag-N-drop

Select precision* of answer:

Select angle mode:

Enter expression to evaluate here:

The answer is shown below:

Enter function to be plotted:

f(x) =

Enter 2nd function, if needed:

g(x) =

Change or reset the x-y scaling below:

x_min =

x_max =

y_min =

y_max =

Accuracy Disclaimer

The javascript math object methods used for this calculator are not accurate for very large or very small numbers. In particular, the trigonometric functions may yield very small answers that should actually be zero or very large answers that should be infinite. This typically occurs at 90° or pi/2 intervals.

DO NOT USE WHERE HIGH PRECISION IS REQUIRED. USE AT YOUR OWN RISK.

(Close Window)

In this section we will be transforming each of the parent curves, shown previously in the family of curves section. For each function, moving left to right in each row, the first slide will be the original function and the negative of the function. The next slide is moved up and down. The third is moved left and right. The last one is scaled up or down. For a linear function, note how it is very hard to distinguish a right-left move from an up-down move. For this reason, if you look closely, you can see a couple of dots that have been put on each line to illustrate the difference between the two.

Linear Function Transforms

Negate

Up - Down

Left - Right

Scale

Square Function Transforms

Negate

Up - Down

Left - Right

Scale

Cube Function Transforms

Negate

Up - Down

Left - Right

Scale

Inverse Function Transforms

Negate

Up - Down

Left - Right

Scale

Square Root Function Transforms

Negate

Up - Down

Left - Right

Scale

Absolute Function Transforms

Negate

Up - Down

Left - Right

Scale

Summary

Having examined each of these transforms, hopefully you can draw the following conclusions:

• Negation: Multiplication by (-1) flips the parent function upside down.

• Up-Down: Adding to the function will move it up, subtracting will move it down.

• Left-Right: Adding to 'x' will move it left, subtracting from 'x' will move it right.

•  Scaling: Multiplying the function by a number greater than one (1) will cause the curve to get
   narrower and taller.  Multiplying the function by a number less than one (1) or dividing by a
   number greater than one will cause the curve to get wider and shorter.