Piecemeal Functions Help (1 Viewer)

[cookiez69]

The function f(x) is defined by:

-x+2 if x >= 1
f(x) = x^2 if -1 =<x<1
x+2 if x<-1

i) Sketch the curve y=f(x)
ii) Find the value(s) of x so that:

f(x)= x/2

I've already sketched the curve, I just need help with the second question. Thanks

 

[Shadowdude]

You can solve this graphically.

Get your piecewise function and graph it. Then graph y = x/2, and then where it meets should be your solutions.

 

[cookiez69]

Hmm, my tutor told us it was called Piece meal functions, but that's not the point. Thank you! Much appreciated

 

[Drongoski]

piecewise it is - like Shadow said.

 

[braintic]

They are called BOTH piecemeal and piecewise functions.
Piecemeal is the most commonly used term.

 

[Drongoski]

"piecemeal" got propagated by those who could not get "piecewise" right. A bit like people nowadays saying "could of" where it should have been "could have" or "could've".

 

[braintic]

Mate, I am a teacher, and I'm approaching 50. When I was at school, and for the first 10 years of my teaching career, 'piecemeal' was the only term used in NSW. 'Piecewise' has only crept in the last 15-20 years. 'Piecemeal' is not incorrect (and I'm not saying 'piecewise' is either). It is nothing like saying 'could of'.

 

[Drongoski]

Mate - I just picked up 5 calculus texts : James Stewart, Thomas & Finney, Grossman, Anton et al, Murray Spiegel - all "piecewise".

 

[seanieg89]

Mates, if you are going to argue about mathematics at least argue about something of substance. Terminology varies and it always will. Personally I have seen the word piecewise used MUCH more than piecemeal, but pretty much everyone knows what is meant by the use of either term...so why make a big deal of it?

This happens all over the place in mathematics and is unavoidable when people are educated in different corners of the globe and tailor their books on the sources they learned from.

 

[braintic]

I don't see any references to NSW HSC maths books there - in fact I don't think any are Australian. All I am arguing is that 'piecemeal' was taught in NSW 32 years ago when I was in year 11. Unlike you, I am not arguing that either word is 'wrong'. I believe that you probably did your HSC much more recently, so you would have no evidence of 'piecemeal' creeping in to the maths vocabulary in NSW. That is just guesswork, and at least over the last 32 years is plain wrong.

And seanieg89, if you read my posts you will see I am arguing exactly the same as you. Both words are correct, both words are used, and it makes no sense to compare the use of 'piecemeal' with the use of 'could of'. Nevertheless, I reserve the right to debate anything I see fit.

 

[Shadowdude]

My teacher called one of my English essays 'piecemeal', which means put together scrappily and is of generally low quality. Piecemeal might've been a valid term before, but I think it's obsolete now - and especially with that double meaning of 'low quality'...


I think later on anyway if you continue with maths at university, you'll come across 'piecewise continuous functions' - and I think because of that reason, piecewise is the better word to use because 'piecemeal continuous functions' yields no real results on Google.

 

[Carrotsticks]

It's terminology, who cares?

Inverse trigonometric functions, arcsin(x) , cyclometric functions etc

Best to keep this thread back on track. However, you are welcome to 'dispute' different terminologies in the Extracurricular thread.