diff --git a/include/numerics/analytic_function.h b/include/numerics/analytic_function.h
index 9dfbb27ded..ecaae0f23f 100644
--- a/include/numerics/analytic_function.h
+++ b/include/numerics/analytic_function.h
@@ -111,7 +111,10 @@ inline
 Output AnalyticFunction<Output>::operator() (const Point & p,
                                              const Real time)
 {
-  libmesh_assert (this->initialized());
+  libmesh_assert(this->initialized());
+  libmesh_assert_msg(_number_fptr,
+                     "You must construct AnalyticFunction with a scalar-valued "
+                     "function in order to use this operator() override.");
   return (this->_number_fptr(p, time));
 }
 
@@ -123,7 +126,10 @@ void AnalyticFunction<Output>::operator() (const Point & p,
                                            const Real time,
                                            DenseVector<Output> & output)
 {
-  libmesh_assert (this->initialized());
+  libmesh_assert(this->initialized());
+  libmesh_assert_msg(_vector_fptr,
+                     "You must construct AnalyticFunction with a vector-valued "
+                     "function in order to use this operator() override.");
   this->_vector_fptr(output, p, time);
   return;
 }