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?
Welcome to the forum.
You can add 'hyperbola to your list by looking at
sin, cos, tan at
logs and powers are distinctive. (There are other rarer ones)
You can try these for yourself at
After that, there may not be a name so you may just have to get a sketch to see what the graph looks like.
Well,what would this function's graph look like-
Sorry,there will be '=d' in the right of equation [d=constant]
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.
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?
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.
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.
Yes, I worked that out. No problem and no harm done.
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?
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.
The equation grapher for this is at
Thanks for trying the Latex. But you finish the line with [/math] not [\math]