1.4, 1.5 – Exponential Functions, Math& 151

Logarithms, & Inverse Functions Warnock - Class Notes

Exponential Functions have the form __________________ and their

graphs look like

If: _____________ If: _____________

There is one exponential base that is most convenient when doing

Calculus. Let’s look at 2xy and 3xy .

The m given is the slope of the _______________ __________ at (0,1).

It turns out that Calculus formulas are greatly simplified if the slope of

that tangent line is equal to exactly _______. The value of that base

has been named, e.

We call the function xf x e the

_________________ ___________________

_________________

#1) Graph 2 2xy e .

Inverse Functions

Putting it another way…

So, the Domain of 1f = _____________________

And, the Range of 1f = _____________________

1 _____, _____f f x x AND 1 _____, _____f f x x

#2) Find the inverse function of 5 3f x x .

Logarithmic Functions

#3) Evaluate 2 2

log 80 log 5

Natural Logarithms

#4) Solve the following for x.

a) ln 6x b) 2 7 8xe

#5) Write the following as a single logarithm. 1ln ln3

x y

Review Inverse Trig’s on your own, pages 64-66.