More Curves

RickyOswaldIOW · 2006-09-10 08:31:30

Sketch the graph of the curve with the equation y = 1(1 - x). Determine the greatest and the least values of y when -1 ≤ x ≤ 1.

I can sketch this curve just fine, but what is meant by the last sentance? Is it asking for a set of co-ords on the curve where x = -1 and x = 1?

luca-deltodesco · 2006-09-10 08:58:27

no, what its asking for, is for you to determine, from the graph, what the greatest possible, and smallest possible value that y can be, given that -1 <= x <= 1, so if you look at the graph, just ignore any part of which x isnt in the range, and read off the highest and lowest value of y,

MathsIsFun · 2006-09-10 10:53:04

Shouldn't that be 1/(1 - x) ? A much more interesting curve than 1(1 - x).

Plot of 1/(1-x)

Between x= -1 and 1, min y = 1/2, max y = ∞

RickyOswaldIOW · 2006-09-10 11:01:06

Unfortunately, A-level maths C1 doesn't do "interesting"

RickyOswaldIOW · 2006-09-10 11:10:52

Is it asking for the maximum and minimum points of the curve between x = -1 and x = 1 on the axis? i.e. the maximum point of the curve is (1/2, 1/4) and then the two corresponding points at (-1, y) and (1, y)?

MathsIsFun · 2006-09-10 15:21:08

Am I understanding the equation correctly? 1(1-x) is just 1-x (Plot of 1(1-x))

In that case the greatest value of y is 2 and the least value is 0

luca-deltodesco · 2006-09-10 17:51:29

rickyoswaldiow wrote:

Unfortunately, A-level maths C1 doesn't do "interesting"

where in C1 is this? i couldnt find this question (not that i looked too hard, books too big ;D) unless ofcourse, youre doing different exam board, or just have a different book . (my C1 is for OCR, by Cambridge)

Last edited by luca-deltodesco (2006-09-10 17:52:44)

RickyOswaldIOW · 2006-09-11 13:10:43

EdExcel, NEC - I study from home.

RickyOswaldIOW · 2006-09-11 13:15:23

Am I understanding the equation correctly? 1(1-x) is just 1-x (Plot of 1(1-x))

It's a curve, not a straight line. I don't have the book to hand but it must be x(1-x), typo on my part . The curve is a curve of x².
x(1-x)
-x² + x

If you plot this curve on an axis you can read out the minimum and maximum co-ords of the points between x = -1 and x = 1 i.e. (-1, y), (1, y) and the vertex (1/2, 1/4).

Last edited by rickyoswaldiow (2006-09-11 13:16:13)

RickyOswaldIOW · 2006-09-13 03:01:17

I still don't understand this. So far the book has covered how to sketch the graphs of y=x^2, y=x^3 and y=1/x and how to translate and scale them. It also taught us how to find the vertex point and the points where it intersects the axis. If the question is asking me for the y value at x=-1 then, following what the book has taught so far, I don't know how to do it.
I can work the answer out because I am past this point in the book, I don't know how to work it out using any of the methods the book has taught so far:
Factorising and
Completing the Square

Any ideas?

MathsIsFun · 2006-09-13 12:24:08

So we have Plot of x*(1-x).

In the range -1 ≤ x ≤ 1, the smallest y-value is -2 (at x=-1). But the largest value is at the "top of the hill", looks to be a little above 0.2.

By symmetry I can see that it occurs exactly half way between x=0 and x=1, so it must be at x=0.5

y = x(1-x) = 0.5(1-0.5) = 0.25 DONE

There are other ways to find the maximum y value, if you look towards the end of Completing the Square there is a good example (your quadratic is x²-x, so a=1, b=-1, c=0).

Math Is Fun Forum

#1 2006-09-10 08:31:30

More Curves

#2 2006-09-10 08:58:27

Re: More Curves

#3 2006-09-10 10:53:04

Re: More Curves

#4 2006-09-10 11:01:06

Re: More Curves

#5 2006-09-10 11:10:52

Re: More Curves

#6 2006-09-10 15:21:08

Re: More Curves

#7 2006-09-10 17:51:29

Re: More Curves

#8 2006-09-11 13:10:43

Re: More Curves

#9 2006-09-11 13:15:23

Re: More Curves

#10 2006-09-13 03:01:17

Re: More Curves

#11 2006-09-13 12:24:08

Re: More Curves

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