Transformations: modulus, and functions of periodic functions

I’ve started a new series on transformations, and three videos are up already. I prioritised what I think will help the most over the next few days, so they’ve been made in a weird order!

In Part 3: Various modulus transformations, we look at what changes when the modulus goes inside a function, outside it, or around $y$: $y = |f(x)|$, $y = f(|x|)$ and $|y| = f(x)$. We then treat $|x - a|$ as a distance, which makes sums of moduli and their minimum values much easier to see, and finish with two questions from the JZMaths mock papers.

In Part 5: Functions of Periodic Functions, we sketch graphs such as $\sin(\cos x)$ and $\cos(\sin(\cos x))$ by working from the inside out, and finish by counting the solutions of $\cos(\sin(\cos x)) = \sin(\cos(\sin x))$.

The Part 5 bonus takes the ideas further with a quadratic function of $\sin x$ and a rational function of $\cos x$. Treat it as enrichment rather than typical TMUA material.

Watch Part 3 · Watch Part 5 · Watch the Part 5 bonus · Browse all videos