how todo curve sketching?

Question

i exactly dont know how to plot a curve on graph

Answer 1

Depending on your grade
1- Determine the points of maximum and minimum values for your function ( using differential calculus)
2- Determine the points of inflection
3- Determine the increasing and decreasing intervals
4- Determine the convex and concave intervals
5- Get the points of intersection with x,y axis
6- Get more points around the critical points you get
7- Sketch the curve using all points you get

Answer 2

Not sure on your level of maths but basically the simplest way to draw a graph is to do the following:

1. Look for easy points, ie: when x=0 and/or y=0, x=1 y=1 etc (where x and y are your equation variables).

2. What happens when x/y approaches infinity (ie becomes large). So basically sub in a huge value of x and/or y into your equation and see what happens, your equation will usually approach zero( become very small), approach infinity (become very large) or approach some other value. Also do the same but for when x/y become very small, ie approach zero

3. Look for any asymptopes etc. Ie suppose your equation is y=ln(x) it follows that x>0. or if you have y=1/x the value of x=0 is an asymptote to the curve because at x=0 y=infinite. SO basically look for undefined values and the arguments of certian functions, sin, cos,tan etc..

4. Calculus: differentiate and find any turning points and points of inflection and their nature( not always nessecary to determine nature because if you have enough info it should be obvious)

5. Loos for any symmetries and/or periodic functions etc,, such as the trig functions etc.

Put together!

If you get really stuck just plot a few values to give you a general shape.

Answer 3

make a table of values of x and y

draw x and y axes.
plot the points. join them and draw the graph.