The derivative of  is:

Let . The graph of has:

If and , then the maximal domain of the function is:

For the functions and , the following is true:

The value of equals:

Over the interval  has exactly one asymptote.

The equation of the asymptote is:

Let .

The period and the range of this function are, respectively

Let and . The solutions for such that where are:

A transformation maps the point to the point .

The transformations in order are:

• Dilate from the -axis of factor .

• Reflect in the

  -axis.

• Translation

  unit in the positive -direction.

• Translation

  units in the negative -direction.

The point has the coordinates:

The value(s) of that make the equation true is

The value of that makes the equation true is