sketch

[red and white kop!]

i am told in my book, in the middle of a domain/range section:
sketch the graph of x(8-2x)(22-2x)
i really have no idea of how to do this, any tips?

 

[galactus]

Domain is what goes in and range is what comes out. Graph it with a calculator.

 

[Deleted member 4993]

i am told in my book, in the middle of a domain/range section:
sketch the graph of x(8-2x)(22-2x)
i really have no idea of how to do this, any tips?

If your problem is really to sketch:

\(\displaystyle f(x) = x(8-2x)(22-2x)\)

Then I'll note that the range and the domain of the function is \(\displaystyle (-\infty, \infty\) - there is really no "middle" to this set.

Then I'll note that the function has zeroes at x = 0, 4 and 11

Then, I'll evaluate the function at x = 2 and x = 7.5.(these are local max/min)

Then I'll plot the function with x = -1 to 12 and the range would go beyond including those max/min.

 

[BigGlenntheHeavy]

\(\displaystyle f(x) \ = \ 4x^{3}-60x^{2}+176x \ = \ 4x(x-11)(x-4), \ a \ polynomial \ of \ degree \ 3.\)

\(\displaystyle See \ graph \ below, \ courtesy \ of \ Maple \ 8, \ it \ should \ be \ self-explanatory.\)

[attachment=0:29foycpu]jkl.jpg[/attachment:29foycpu]

 

[mmm4444bot]

\(\displaystyle (-\infty, \infty)\) -- there is really no "middle" to this set.

I think the poster was referring to a section in their textbook versus a section of an interval. (heh, heh, heh)

More interesting to me here is the notion that zero might not be the midpoint of the Real number line. I've always thought of zero like that, when thinking graphically. Is this perception wrong?

 

[BigGlenntheHeavy]

\(\displaystyle mmm4444bot, \ according \ to \ Cantor, \ there \ are \ different \ infinities, \ so \ where \ 0 \ might \ be \ the\)

\(\displaystyle \ midpoint \ of \ one, \ it \ isn't \ necessary \ so \ that \ it \ is \ the \ midpoint \ of \ another.\)

 

[Deleted member 4993]

Re:

\(\displaystyle (-\infty, \infty)\) -- there is really no "middle" to this set.

I think the poster was referring to a section in their textbook versus a section of an interval. (heh, heh, heh)

More interesting to me here is the notion that zero might not be the midpoint of the Real number line. I've always thought of zero like that, when thinking graphically. Is this perception wrong?

You are correct. But for infinite line, every point is mid-point, including zero.

 

[red and white kop!]

umm, i guess i will stick with the local max/min and x-axis intercepts...

 

[mmm4444bot]

umm, i guess i will stick with the local max/min and x-axis intercepts...

Yes, follow Subhotosh's reasoning. Since polynomials are easy to evaluate, I would only add that it's relatively easy to make a table of (x, y) values for x = Integers from -2 to 12. That would give you plenty of points to "see" the shape of the curve, when graphing by hand.

I didn't mean to sidetrack your discussion with my post. I'll move my ramblings to a more appropriate area.