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**Wink****Guest**

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?

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,662

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 … =-8&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

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Mint****Guest**

Well,what would this function's graph look like-

**Mint****Guest**

Sorry,there will be '=d' in the right of equation [d=constant]

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,662

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

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**zetafunc.****Guest**

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?

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,662

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

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Mint****Guest**

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.

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,662

Yes, I worked that out. No problem and no harm done.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Mint****Guest**

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?

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,662

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

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