Family of Curves

Subject Areas

Tools / Misc

bCalc

drag-N-drop

scrnGC2: Calc Input

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.

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Family of Curves

The graphs shown below are six basic parent curves that constitute a family of curves. Knowing these curves and how they can be transformed can help you in visualizing functions before you even bother to graph them.

Linear: f(x) = x

Square: f(x) = x²

Cube: f(x) = x³

Reciprical: f(x) = 1 / x

Square Root: f(x) = √ x

Absolute Value: f(x) = | x |

Each one of these curves can be duplicated using the graphing calculator that is provided for you on this page. With the exception of the reciprical function, all the other functions pass throught the origin. The reicprical function may appear to pass through the origin but it is just how the graphics routine switches from -Infinity to +Infinity.

The critical thing to remember besides the basic shapes is that these can be viewed as transparencies with a fingerhole placed at the origin. This is very important because as we move on to transformations, you will find that you will simply be sliding these curves left-right, up-down or flipping them.

Once you understand this basic family of curves, see how easy it is to manipulate them by going to the next section, transformations.