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Feb. 19th, 2009 09:15 pmWow, I'm just astoundingly annoyed with my sister's maths teacher.
So, they're doing hyperbolas in class at the moment. For those who don't remember (why would you?) these graphs take the form of y =a/(x + b) + c. (This isn't strictly true, but it's true enough for this class.) These graphs have an x-asymptote and a y-asymptote, and obviously one of the things you have to work out is what these asymptotes are - the places where the equation is undefined. The y asymptote is pretty easy - it's c. (NOTE: there is a better, more maths-y, and more generalisable explanation which is that a y-asymptote is the limit of a function f(x) as x tends towards infinity, but while I understand this and can even demonstrate it on paper I can't do it in a livejournal entry. So this is the fifth form maths explanation.) That's because, no matter what x is, c + (a/x) /=/ c (unless a/x = 0, but since a is not a variable that's not possible.) So y can never = c, and the y asymptote is the line y=c. The x asymptote is slightly harder; it occurs when the fraction a/(x + b) is undefined, which happens when the denominator is 0. (For the record: her maths teacher is so fucking shitty that, when I asked my sister what a/0 was, she said "zero." um, NO. if your teacher didn't jump up and down at the front of the class hyperventilating about how that fraction is undefined, that teacher SUCKS.) At any rate, the x-asymptote is x = -b.
But do you know what her teacher was doing? He was drawing hyperbolas, adding a +c value to the equation, and drawing the hyperbola again. UM, NO. This is like telling someone the formula for the hyperbola and then telling them that the asymptotes are c and -b, without ever explaining why that is true. You know why this is totally shitty teaching? Because if that student gets into an exam and tries to remember what y and x asymptotes are, if they happen to have forgotten your little gem, they have no grounds for *working out* what the asymptotes are. And that? is fucking dumb. I had to teach my sister this tonight in order to get her to do her homework because until I did, she didn't understand what she was doing, and consequently didn't know how to do it. DUMB. asdfgh.
So, they're doing hyperbolas in class at the moment. For those who don't remember (why would you?) these graphs take the form of y =a/(x + b) + c. (This isn't strictly true, but it's true enough for this class.) These graphs have an x-asymptote and a y-asymptote, and obviously one of the things you have to work out is what these asymptotes are - the places where the equation is undefined. The y asymptote is pretty easy - it's c. (NOTE: there is a better, more maths-y, and more generalisable explanation which is that a y-asymptote is the limit of a function f(x) as x tends towards infinity, but while I understand this and can even demonstrate it on paper I can't do it in a livejournal entry. So this is the fifth form maths explanation.) That's because, no matter what x is, c + (a/x) /=/ c (unless a/x = 0, but since a is not a variable that's not possible.) So y can never = c, and the y asymptote is the line y=c. The x asymptote is slightly harder; it occurs when the fraction a/(x + b) is undefined, which happens when the denominator is 0. (For the record: her maths teacher is so fucking shitty that, when I asked my sister what a/0 was, she said "zero." um, NO. if your teacher didn't jump up and down at the front of the class hyperventilating about how that fraction is undefined, that teacher SUCKS.) At any rate, the x-asymptote is x = -b.
But do you know what her teacher was doing? He was drawing hyperbolas, adding a +c value to the equation, and drawing the hyperbola again. UM, NO. This is like telling someone the formula for the hyperbola and then telling them that the asymptotes are c and -b, without ever explaining why that is true. You know why this is totally shitty teaching? Because if that student gets into an exam and tries to remember what y and x asymptotes are, if they happen to have forgotten your little gem, they have no grounds for *working out* what the asymptotes are. And that? is fucking dumb. I had to teach my sister this tonight in order to get her to do her homework because until I did, she didn't understand what she was doing, and consequently didn't know how to do it. DUMB. asdfgh.
