Test will cover Modules 12, 13, 14, and 15

 Remember that logs of numbers are still just numbers. Please don’t turn them into decimals unless instructed otherwise, it’s like leaving a square root as a square root – it’s just prettier!  Do not be afraid of e. It’s just a number too. It just happens to be a super cool number that we can do a lot with.  This rule will be your friend:

 Exponential Functions:  Log Functions:

 You don’t have a chance at doing graphing transformations correctly if you don’t start with the correct parent function. Remember the 4 basic exponential/logarithmic shapes: ◦ If you forget, you can always plug in a couple of points to help you remember which one is which (you can even do this to check that you’ve done a transformation correctly!)

 Also, remember the vertical and horizontal asymptotes of the parent functions to make it easier to see the asymptotes in the transformed ones.

Domain: all reals Range: (0, infinity) Domain: all reals Range: (0, infinity) Domain: all reals Range: (0, infinity) Domain: all reals Range: (0, infinity) Domain: (0, infinity) Range: all reals Domain: (0, infinity) Range: all reals Domain: (0, infinity) Range: all reals Domain: (0, infinity) Range: all reals

 Vertical Adjustments ◦ f(x) + c  Moves graph up c units ◦ f(x) – c  Moves graph down c units ◦ 2*f(x)  Stretches vertically by a factor of 2  (could be any number > 1) ◦ 0.5*f(x)  Compresses vertically by a factor of 2  (any fraction between 0 and 1) ◦ -f(x)  Reflection over the x axis

 Horizontal Adjustments  (usually backwards from what you expect) ◦ f(x + c) left  Moves graph left c units ◦ f(x – c) right  Moves graph right c units ◦ f(2*x)  Compresses horizontally by a factor of (1/2)  (could be any number > 1) ◦ f(0.5*x)  Stretches by a factor of 2  (any fraction between 0 and 1) ◦ f(-x)  Reflection over the y axis