# Graphs

## Exponential Growth: Surprisingly Flexible

Two recent questions from the same student involve exponential functions: We can express different kinds of growth all using one base, called e; or we can use different bases (and ignore horizontal scaling transformations). And we can use different transformation to obtain the same graph. This relates to some important properties of exponential functions.

## The Shape of a Polynomial at its Zeros

Last week’s discussion about zeros of a polynomial, and other conversations, have reminded me of a past discussion of the shape of the graph of a polynomial near its zeros. Let’s take a look, starting with some other questions that nicely lead up to it.

## Is That Really a Polynomial?

(A new question of the week) We often see polynomials in a simplistic way, imagining that any function whose graph resembles a polynomial is a polynomial. Much as an attempt to mimic random data often lacks essential properties of genuine randomness, so what we intend to be a polynomial often is not. As we observe …