D.I.S.A.C.

 

D:  [Domain]   set denominator equal to zero, then x cannot be the values.  If no denominator, all real numbers

 

I:   [intercepts] x-intercept: set numerator equal to zero and solve (if easy)

                        y-intercept:  put zero in for x

 

S:  [symmetry]:  even or odd

 

A:  [asymptotes]:  find vertical by setting denominator equal to zero

                              Find horizontal by dividing everything by the largest exponent in denominator

                             Finding slant:  do long division

 

C:  [calculus]:  use 1st derivative to find increase/decrease, use 2nd derivative to find concave up and concave down.

 

 

Example:

 

 

Domain:  x = all real numbers

 

Intercepts:  y = 2

 

Symmetry:  no symmetry (because the +2 moves function away from origin)

 

Asymptotes: no denominator means any asymptotes

 

Calculus: 

 

*                                           increasing from –1 to 1

                                                            decreasing from to –1, and 1 to

 

 (-)      (+)       (+)   (-)

 

                                      concave up from to 0

                                                            concave down from 0 to

    (+)            (-)