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