Math Is Fun Forum

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,648

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 … =-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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Mint

Guest

Re: Graph of a function

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

Mint

Guest

Re: Graph of a function

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,648

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

---

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,648

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

---

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,648

Re: Graph of a function

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

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,648

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

---

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob