When do you round up/down in maths?
Let me give you an example. Just say,
Where is the graph below y = 30?
And you get 1.3 < x < 3.6 (imagine parabola) and it says to the nearest integer.
If you round normally and do 1 < x < 4, it's not entirely correct to say this is where the graph is below y = 30, because portions of it isn't.
So would you round to 2 < x < 3 to satisfy the condition or not? I'm super confused because in one maths test you did have to round to satisfy, and another you didn't ...
Or perhaps it makes a difference in saying 'to the nearest integer' and 'where x is an element of the integer set'?
March 25, 2014
11 Comments • Newest first
And this is why I don't do maths.
[quote=MyTiramisu]Would it help if I said, find all x values such that y < 0[/quote]
Can you copy of an exact question that you got from your textbook or something? It will be better to explain that way I guess.
[quote=esporteen]After reading what he is saying for like 50times now, I think I understand what you meant.
Basically he is trying to look for a "boundary" (think of asymptotes) for which includes the graph he is given is included. (ie, looking for a subset within a set but let's not dwell into that).
But one thing to fully understand the question, are you given a SPECIFIC point in a graph where you have to find such boundary? It's a bit vague if you are just given the equation of the graph then you'd be asked to get the boundaries as it might be more complicated than just a simple x is between two numbers (ie, if you want to get a "boundary" of y = x^2 above the x axis it will be -infinity<x<+infinity as it goes on forever)[/quote]
Would it help if I said, find all x values such that y < 0
After reading what he is saying for like 50times now, I think I understand what you meant.
Basically he is trying to look for a "boundary" (think of asymptotes) for which includes the graph he is given is included. (ie, looking for a subset within a set but let's not dwell into that).
But one thing to fully understand the question, are you given a SPECIFIC point in a graph where you have to find such boundary? It's a bit vague if you are just given the equation of the graph then you'd be asked to get the boundaries as it might be more complicated than just a simple x is between two numbers (ie, if you want to get a "boundary" of y = x^2 above the x axis it will be -infinity<x<+infinity as it goes on forever)
@strenling: Oh oops, yup it's supposed to be -1.
If it says nearest integer, I'd go to the nearest, even if it was technically out of your range, because he only wants your range to the nearest integer clearly.
[quote=MyTiramisu]Okie let me try and do a more understandable one. How bout y = (x - 4.6)(x + 1.6) and you're trying to work out where the graph is below the x-axis. But, your answer must be to the nearest integer. The intercepts are (4.6, 0) and (-1.6, 0) which would generally mean your answer after rounding is -2 < x < 5, however that's not entirely correct because portions of that would not be below the x-axis, so would you instead round to 1 < x < 4 so that it satisfies the condition, below the x-axis?[/quote]
With that graph, all of the space between the x-intercepts are below the X-Axis, I dunno about what you're talking about there.
But yeah, since the intercepts are -1.6 and 4.6, and since you're told (oddly) to round to the nearest answer, I guess your answer would be -2<x<5 ~ However, it might be the case that you have to round down (for reasons like real life counting. You can't say you need 150 seats when you have 153 people, just because of rounding.) - Whereas your answer would be -1<x<4.
EDIT: Ohh, I see what you're trying to say now. - Did you accidentally put the second to positive 1 when you meant to have negative ('...so would you instead round to 1 < x < 4..." )- If so, that's probably the case.
Round down.
Rounding up includes incorrect values.
Hmm, your English is a bit weak but I get what you're saying.
I have never heard of a math class that wants you to round the ranges for the answer, but I would use the range that is definitely under the plot point for full accuracy, but low precision. It would be up to what your teacher wants.
[quote=strenling]Oi. My brain hurts from trying to figure out what you're trying to say.
First off, what's the original equation? Just a standard parabola? y=x^2?
If so, the domain that's below y=30 would be about -5.45<x<5.45 (In a nicer form, (-5.47, 5.47)..). Don't exactly know how to help.[/quote]
Okie let me try and do a more understandable one. How bout y = (x - 4.6)(x + 1.6) and you're trying to work out where the graph is below the x-axis. But, your answer must be to the nearest integer. The intercepts are (4.6, 0) and (-1.6, 0) which would generally mean your answer after rounding is -2 < x < 5, however that's not entirely correct because portions of that would not be below the x-axis, so would you instead round to 1 < x < 4 so that it satisfies the condition, below the x-axis?
Oi. My brain hurts from trying to figure out what you're trying to say.
First off, what's the original equation? Just a standard parabola? y=x^2?
If so, the domain that's below y=30 would be about -5.45<x<5.45 (In a nicer form, (-5.47, 5.47)..). Don't exactly know how to help.