# Browsing category graphs

## A curve-sketching masterclass

An implicit differentiation question dealt with $y^4 - 2x^2 + 8xy^2 + 9 = 0$. Differentiating it is easy enough for a competent A-level student - but what does the curve look like? That requires a bit more thought. My usual approach to sketching a function uses a structure I

## Ask Uncle Colin: Are normals… normal?

Dear Uncle Colin, I don't understand why the normal gradient is the negative reciprocal of the tangent gradient. What's the logic there? -- Pythagoras Is Blinding You To What's Obvious Hi, PIBYTWO, and thanks for your message! My favourite way to think about perpendicular gradients is to imagine a line

## The Great Straight Lines debate

* Edited 2016-10-24 to add categories, just for Cav.

## A curve-sketching challenge

Via @DrTrapezio, an interesting question: Year 13 curve sketching challenge: y = | | | |x| - 1| - 1| - 1| — Luciano Rila (@DrTrapezio) July 14, 2016 Where do you even start with that mess? The answer to that, my friend, is you start in the middle and

## Ask Uncle Colin: Finding a curve with an asymptote

Dear Uncle Colin, I'm looking for the equation of a curve that goes through the points $\left(10, \frac{1}{64}\right)$ and $\left(100, \frac{1}{32} \right)$, as -- as $x$ gets large -- approaches 1. How do I go about it? Always Silence Your Mobile Phone Typing Out Tricky Equations Good advice, ASYMPTOTE! And

## Rewriting a function without going piecewise

You know the ridiculous kind of pseudo-context question that makes you go 'Why doesn't Lisa get a proper hobby rather than timing her friends doing jigsaw puzzles?'? You could replace pretty much all of them with "A mathematician is trying to be clever by...". In this particular case, a mathematician

## The Maths Police (Financial Unit) Investigate

A guest post from @FennekLyra, who is Eva in real life. Thanks, Eva! “Want to see something awful?” asked Agent Lyra1 suddenly, turning to her fellow maths agent and friend Dodo at the £16,000 question of Who Wants To Be A Millionaire? that both of them watched daily. “Oh come

## Ask Uncle Colin: An imaginary curve?

Dear Uncle Colin, I was playing with parametric equations and stumbled on something Wolfram Alpha wouldn't plot: $x=t^i;\, y = t^{-i}$. Does this curve really exist? Or am I imagining it? -- A Real Graph? A Non-existant Drawing? Hi, ARGAND -- what you're trying to plot certainly exists; whether or

## A great student question

Most of the time, my goal as a tutor is to help students stop hating maths and, if I'm lucky, to grudgingly accept that there are some good bits to it. I'm not here to indoctrinate anyone into becoming a mathematician unwillingly. And then sometimes, I get asked a question

## Maths Police Christmas Special

In which @reflectivemaths and I find out which graphs have been naughty and nice. Hint: none of them are nice. Constable Gale blew a party streamer and I shot him a steely glare. "Are you hanging up your stockings on the waaaalll?" he crooned. "No, Gale. I am decidedly not