Graphing

A Mind-Stretching Exercise with a Stretched Cosine

(A new question of the week) A question in September, about graphing a horizontally-stretched cosine function, led to a long conversation. Between a typo in the problem and some inside-out thinking, this surprisingly non-routine problem led to some good mind-stretching! I have edited this down considerably by removing distractions from the main ideas, but it …

A Mind-Stretching Exercise with a Stretched Cosine Read More »

Reading Pandemic Graphs

(A new question of the week) Having just discussed several mathematical topics that lie behind the various graphs we have seen in the news lately, I want to depart from our usual style and answer my own current questions. We’ll look at several graphs of COVID-19’s growth and think about what we can learn from …

Reading Pandemic Graphs Read More »

Logarithmic Graphing

We’ve been looking at the math underlying some of the graphs associated with the COVID-19 pandemic, starting with exponential growth, and then logistic growth. I want to look in more detail at a feature I mentioned in the first post, viewing a graph logarithmically. This is a powerful technique that goes far beyond a button …

Logarithmic Graphing Read More »

Exponential Growth

The term “exponential” has gone viral, so to speak. Do we all know what it means? In the next few posts I’ll look at answers we’ve given to questions about exponential growth and related concepts, some of them about the spread of diseases or rumors. (Disclaimer: I will be writing about the basic math, not …

Exponential Growth Read More »

Graphing Transformed Sines

I’ll close out our look at transformations of functions with some trigonometric graphs. These are the best example of combined transformations, and involve some special tricks as well. We’ll start with an early question that gives an overview of the process, then focus in on important details.

Equivocal Function Transformations

The last two posts were about transformations of functions (shift, stretch, reflect) and their effect on a graph, first individually and then in combination. The next thing to look at will be how to determine the transformations when you are given a graph; but before we take that challenge in general, we need to see …

Equivocal Function Transformations Read More »