Graph offunction

Mathematically,graph offunction iscollectionall pairs (x, f(x)) offunction. Graphingsometimes referredas curve sketching.

The graph offunction

is {(1,a), (2,d), (3,c)}.

The graph ofcubic polynomial onreal line

is {(x,x³-9x) : x isreal number}. Ifsetplotted onCartesian plane,result is

Image::cubicpoly.png

Thereforegraph offunction on real numbersidentical tographic representation offunction. For general functions,graphic representation cannot be applied andformal definition ofgraph offunction suitsneedmathematical statements, e.g.,closed graph theoremfunctional analysis.

The concept ofgraph offunctiongeneralised tograph ofrelation. Note that althroughfunctionalways identifiedits graph, theynotsame becausewill happen two functionsdifferent codomain could havesame graph. For example,cubic polynomial mentioned above issurjection if its codomain isreal numbers but itnot if its codomain iscomplex field.

See also:

• concavity
• critical point
• derivative
• extrema
• slope
• solution point
• vertical translation