plz help with this question (1 Viewer)

[muttiah]

could some1 please help me with the concept of the continuity of a curive..

and what does this question mean?

For what values of a are these functions continous :

a) f(x) { ax^2, for x less than or equal to 1 and 6 - x, for x > 1


looks messy plz write it down loosk easier..

if u have the cambridge book then its page 272 question 8(a)

thanks!

 

[edwardpham_2000]

i think you need to find the value of ax^2 that passes through (1,5), since if u sketch y = 6-x it passes through (1,5)

so

ax^2 = 5
let x=1

a = 5

 

[muttiah]

how did u get the point (1,5)
?

 

[SoulSearcher]

Because the curve, follows the line y = 6-x when x > 1, therefore you have to find the point where it first starts, i.e. when x = 1, therefore y = 6-1 = 5

 

[Affinity]

could some1 please help me with the concept of the continuity of a curive..

and what does this question mean?

For what values of a are these functions continous :

a) f(x) { ax^2, for x less than or equal to 1 and 6 - x, for x > 1


looks messy plz write it down loosk easier..

if u have the cambridge book then its page 272 question 8(a)

thanks!

I guess heuristically, being continuous at the 2 unit level is being able to draw the curve pass a point without lifting one's pen (ofcourse in general this will be wrong, but if you restrict the functions to what you use in 2U then it works)

As with the function in the question, it's the simplest way to write it.. perhaps you have to abandon the idea that functions are something tha you can specify by a nice formula.. for example think about how you would write tax payable as a function of income

You would probably end up with:

for 0<=i <= 6000, T(i) = 0
for 6000 < i <= ? T(i) = r*(i-6000)
then something different for the next bracket and so on.


Try to think of a function as a computer or something.. you give it an input, it gives you an output.. and for the same input, the output will be the same.


now if you read

For what values of a are these functions continous :

a) f(x) { ax^2, for x less than or equal to 1 and 6 - x, for x > 1

just think of it literally. .. f(x) is just a rule giving some output for each x.

for example what is f(-2)? if you look at the question, -2 is less than or equal to 1. therefore the rule x +--> ax^2 applies., so f(-2) = 4a
what is f(1)? 1 is less than or equal to 1, so f(1) = a*1^2 = a
what is f(3)? r is greater than 1, so f(3) = 6-3 = 3

etc..

 

[muttiah]

thanks i got it now!