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#1 2012-10-28 17:07:15
- Wink
- Guest
Graph of a function
Is there a method to recognize what a function's graph will be by just looking at the equation?I know how to recognize circle,ellipse,line,parabola,what about others?
#2 2012-10-28 19:24:34
- bob bundy
- Moderator
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Re: Graph of a function
hi Wink,
Welcome to the forum.
You can add 'hyperbola to your list by looking at
http://www.mathisfunforum.com/viewtopic.php?id=18300
sin, cos, tan at
http://www.mathsisfun.com/algebra/trig- … raphs.html
logs and powers are distinctive. (There are other rarer ones)
You can try these for yourself at
http://www.mathsisfun.com/data/function … amp;ymax=8
After that, there may not be a name so you may just have to get a sketch to see what the graph looks like.
http://www.mathisfunforum.com/viewtopic.php?id=15139
post 7.
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#4 2012-10-28 23:33:38
- Mint
- Guest
Re: Graph of a function
Sorry,there will be '=d' in the right of equation [d=constant]
#5 2012-10-28 23:36:33
- bob bundy
- Moderator
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Re: Graph of a function
hi Mint
I noticed an identical post but with an email address. This is not encouraged so I've deleted the duplicate.
I think the answer may depend on the exact values of a, b, c and d.
I'll have a think and post back when I've got something more to say.
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#6 2012-10-28 23:39:09
- zetafunc.
- Guest
Re: Graph of a function
Generally it is difficult to say what the general graph of something of that form would look like. Curve sketching is done by observing properties of the graph:
-Does it have horizontal, vertical or oblique asymptotes?
-Where is the function increasing or decreasing? Are there any points of inflection?
-Where are the turning points?
-Where does it cross the x and y-axes?
-What happens as x approaches positive or negative infinity?
-For what domain and range is your function defined?
#7 2012-10-28 23:41:03
- bob bundy
- Moderator
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Re: Graph of a function
hi again,
It's the equation of a conic section, but which will depend on the coefficients.
eg a = c and b = 0, and d > 0 will produce a circle.
Same but with a ≠ c will be an ellipse.
a > 0 and c < 0 is a hyperbola.
and so on.
http://en.wikipedia.org/wiki/Conic_sections
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#8 2012-10-28 23:47:58
- Mint
- Guest
Re: Graph of a function
Sorry,bob bundy,I had put email address in place of name by mistake,and I didn't know how to delate a post,so I gave another post by mint.
#10 2012-10-29 00:10:13
- Mint
- Guest
Re: Graph of a function
Thank you,I read the article(there cannot be a parabola with my equation,right?).
But,what if,[math]a,b,c,d>0[\math]and they aren't same?
#11 2012-10-29 00:49:32
- bob bundy
- Moderator
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Re: Graph of a function
hi Mint,
I cannot make a parabola from that. That isn't a proof that it's impossible though.
Mostly I got a hyperbola or two straight lines if d = 0.
Examples below.
The equation grapher for this is at
http://www.mathsisfun.com/data/grapher-equation.html
Thanks for trying the Latex. But you finish the line with [/math] not [\math]
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei