Is Zero Positive or Negative? Even or Odd?
Last week we looked at some basics about zero; now let’s look at whether zero is positive or negative, and then at the topic of the recent comment that triggered this series: whether zero is even or odd.
Is Zero Really a Number?
A recent comment on the site raised questions about zero, beyond what we have discussed in the past about division by zero. Here we’ll look at basic questions about whether zero is actually a number at all, and then about multiplication by zero, which confuses a lot of people.
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.
Polynomials: A Matter of Degrees
Last time we examined why polynomials are defined as they are. This time, let’s look at some tricky aspects of the concept of “degree”, mostly involving something being zero.
Polynomials: Why Are Terms What They Are?
A question last week (Hi, Zahraa!) led me to dig up some old discussions of how we define a polynomial (or monomial, or term) and, specifically, why the exponents have to be non-negative integers. Why can we only multiply, and not divide by, variables? Since we’ve been looking at polynomials, let’s continue.
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.
Why Proof Matters: Polynomial Zeros and Turning Points
A recent question from a student demonstrates that not everything on the Internet should be taken at face value – and that it’s easy to think you are right when you are not.
Intersecting Powers and Roots
Here is an interesting little question. Its answer is simple, and not hard to see just by graphing examples; yet the algebra is easy to get wrong, as we’ll see several times. And subtle errors deserve study.
Boxes, Whiskers, and Outliers
Last week we looked at one way to display data, the stem-and-leaf plot. This time, we’ll look at a very different one, the box-and-whisker plot, which summarizes the data more broadly.
Stems, Leaves, and Data
It’s been a while since we’ve written about statistics, so I want to start a short series about that. Here, we’ll look into stem-and-leaf plots (also called stemplots).