IANS Graphing

IANS stands for (Intercepts, Asymptotes, Number Line, Sketch)

 

Therefore first find the asymptotes, find the x-intercepts, put them on a number line and find out where the function is positive or negative, then sketch.

 

Example:

 

Y = (x^2+x-6)/(x+4) OR Y = ((x+3)(x-2))/(x+4)

 

Intercepts:

Asymptotes

 

Number line

 

[-]        (-4)     [+]       (-3)     [-]        (2)      [+]

 

 

Sketch

 

When Sketching, plot all the known points (Intercepts) and the asymptotes (in this case VA at x=-4 and the Oblique Asymptote y=x-3). Then follow the signs on the number line to graph through the intercepts with respect to the asymptotes.

 

 

 

 

 

 

If you have any questions, leave them in the comments below.