the square root of a function will only be defined for values where the function is positive.
25
Expression 26: StartRoot, sin left parenthesis, "x" , right parenthesis , EndRootsinx
26
Expression 27: StartRoot, cos left parenthesis, "x" , right parenthesis , EndRootcosx
27
the sum or product of functions will only be defined when both functions are defined.
28
Expression 29: StartRoot, cos left parenthesis, "x" , right parenthesis , EndRoot StartRoot, sin "x" , EndRootcosxsinx
29
Expression 30:
30
Expression 31:
31
Expression 32: "d" minus StartAbsoluteValue, "x" minus "f" , EndAbsoluteValued−x−f
32
Expression 33: StartFraction, StartAbsoluteValue, "d" minus StartAbsoluteValue, "x" minus "f" , EndAbsoluteValue , EndAbsoluteValue Over "d" minus StartAbsoluteValue, "x" minus "f" , EndAbsoluteValue , EndFractiond−x−fd−x−f
33
This function is 1 for d units left and right of x=f, and -1 everywhere else.
34
Expression 35: "d" equals 1d=1
negative 10−10
1010
35
Expression 36: "f" equals 2f=2
negative 10−10
1010
36
Just play around with the sliders.
37
Expression 38: StartRoot, StartFraction, StartAbsoluteValue, "d" minus StartAbsoluteValue, "x" minus "f" , EndAbsoluteValue , EndAbsoluteValue Over "d" minus StartAbsoluteValue, "x" minus "f" , EndAbsoluteValue , EndFraction , EndRootd−x−fd−x−f
38
This is 1 for those conditions and undefined everywhere else.
39
We can multiply this chunk by any function we like, and it'll apply a domain restriction.
40
Expression 41: StartFraction, tan left parenthesis, "x" , right parenthesis Over 10 , EndFractiontanx10
41
Expression 42: StartFraction, tan left parenthesis, "x" , right parenthesis Over 10 , EndFraction StartRoot, StartFraction, StartAbsoluteValue, "d" minus StartAbsoluteValue, "x" minus "f" , EndAbsoluteValue , EndAbsoluteValue Over "d" minus StartAbsoluteValue, "x" minus "f" , EndAbsoluteValue , EndFraction , EndRoottanx10d−x−fd−x−f