IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

hardcore_genius

how can we draw the graph of a 3 degree(or generally) n degree function???

piyachopra

Graph of f(x) = x³:

f(x) = x³ is cube function
domain

R
Range

R

u can also check it at study material--functions and graph...and if then too u r having problem in graphs then just put values in 'x' n find values of y plot them on graph....

ramyadiamond

For even powered functions,

of the type x²ⁿ, n N, The graph is similar to y=x², but there are slight changes in the curvature of the graph. The curve may be more straightened up, or maybe more curved.The graph will be symmetrical about y-axis.

U can decide it by the given domain of the question, as

x²>x⁴>x⁶>x⁸............... when, -1<x<1

and x²<x⁴<x⁶...................

when x lies b/w -infinity to -1, and 1 to infinity

In case of odd funtions, of the type, x^2n-1,

the graph is symmetrial about origin and extends in opposite quadrants. For reference u can take y=x³, and as before there will be changes in the curvature of the graph, but the pattern remains the same.

for, 1<x<infinity,

x<x³<x⁵.........

for, 0<x<1,

x>x³>x⁵...........

for, -1<x<0,

x<x³<x⁵..........

for, -infinity<x<-1,

x>x³>x⁵..........

Hope this helps

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