Basic Examples 
(6)
 

Compute the points of discontinuity of a rational function:
In[9]:=
[◼]
FunctionDiscontinuities
[(x-3)/(x+4),x]
Out[9]=
{{x-4}}
Repeat the calculation, classifying the points of discontinuity:
In[10]:=
[◼]
FunctionDiscontinuities
[(x-3)/(x+4),x,"Properties"]
Out[10]=
{{x-4,TypeInfinite discontinuity,LeftLimit∞,ValueAtDiscontinuityComplexInfinity,RightLimit-∞}}
———
Compute the points of discontinuity of a trigonometric function:
In[11]:=
[◼]
FunctionDiscontinuities
[Tan[x],x]
Out[11]=


1
∈&&xπ
1
2
+

1

Repeat the calculation, classifying the points of discontinuity:
In[12]:=
[◼]
FunctionDiscontinuities
[Tan[x],x,"Properties"]
Out[12]=


1
∈&&xπ
1
2
+

1
,TypeInfinite discontinuity,LeftLimit∞,ValueAtDiscontinuityComplexInfinity,RightLimit-∞
———
Compute the points of discontinuity of a smooth function:
In[15]:=
[◼]
FunctionDiscontinuities
[E^x*Sin[x],x]
Out[15]=
{}
———
Compute and plot the points of discontinuity of a rational function:
In[13]:=
f[x_]:=(-12-x+
2
x
)/(8+2x-5
2
x
+
3
x
);​​
[◼]
FunctionDiscontinuities
[f[x],x,"Properties"]
Out[14]=
{x-1,TypeInfinite discontinuity,LeftLimit∞,ValueAtDiscontinuityComplexInfinity,RightLimit-∞},{x2,TypeInfinite discontinuity,LeftLimit-∞,ValueAtDiscontinuityComplexInfinity,RightLimit∞},x4,TypeRemovable discontinuity,LeftLimit
7
10
,ValueAtDiscontinuityIndeterminate,RightLimit
7
10

In[16]:=
Plot[f[x],{x,-5,5},ExclusionsStyle{{Red,Dashed},{PointSize0.02}}]
Out[16]=
———
Compute and plot the points of discontinuity of a step function:
In[17]:=
f[x_]:=HeavisideTheta[x];​​
[◼]
FunctionDiscontinuities
[f[x],x,"Properties"]
Out[18]=
{{x0,TypeJump discontinuity,LeftLimit0,ValueAtDiscontinuityHeavisideTheta[0],RightLimit1}}
In[3]:=
Plot[f[x],{x,-5,5},ExclusionsStyle{{Red,Dashed},{PointSize0.02}}]
Out[3]=
———
Compute and plot the points of discontinuity of a step function:
In[19]:=
f[x_]:=Piecewise[{{Sin[x],x<1},{Cos[x],x>1&&x<3}},x-3];​​
[◼]
FunctionDiscontinuities
[f[x],x,"Properties"]
Out[20]=
{{x1,TypeJump discontinuity,LeftLimitSin[1],ValueAtDiscontinuity-2,RightLimitCos[1]},{x3,TypeJump discontinuity,LeftLimitCos[3],ValueAtDiscontinuity0,RightLimit0}}
In[3]:=
Plot[f[x],{x,-5,5},ExclusionsStyle{{Red,Dashed},{PointSize0.02}}]
Out[3]=
———

Options 
(1)
 


Properties and Relations 
(1)
 


Possible Issues 
(1)
 
