diff --git a/aesara/compile/function/types.py b/aesara/compile/function/types.py
index 8aa1e3ee8..d1f9eae2f 100644
--- a/aesara/compile/function/types.py
+++ b/aesara/compile/function/types.py
@@ -785,6 +785,8 @@ class Function:
                 f_cpy.finder[swap[in_ori.variable]] = container
                 in_cpy.variable = swap[in_ori.variable]
 
+        f_cpy.trust_input = self.trust_input
+        f_cpy.unpack_single = self.unpack_single
         f_cpy.name = name
         f_cpy.maker.fgraph.name = name
         return f_cpy

diff --git a/tests/compile/function/test_types.py b/tests/compile/function/test_types.py
index 61322a2e7..ea8b81986 100644
--- a/tests/compile/function/test_types.py
+++ b/tests/compile/function/test_types.py
@@ -299,7 +299,7 @@ class TestFunction:
             t()
 
     def test_copy(self):
-        a = scalar()  # the a is for 'anonymous' (un-named).
+        a = scalar()
         x, s = scalars("xs")
 
         f = function(
@@ -312,26 +312,34 @@ class TestFunction:
         )
 
         g = copy.copy(f)
-        # if they both return, assume  that they return equivalent things.
+
+        assert f.unpack_single == g.unpack_single
+        assert f.trust_input == g.trust_input
 
         assert g.container[x].storage is not f.container[x].storage
         assert g.container[a].storage is not f.container[a].storage
         assert g.container[s].storage is not f.container[s].storage
 
-        assert g.value[a] is f.value[a]  # should not have been copied
-        assert (
-            g.value[s] is not f.value[s]
-        )  # should have been copied because it is mutable.
-        assert not (g.value[s] != f.value[s]).any()  # its contents should be identical
+        # Should not have been copied
+        assert g.value[a] is f.value[a]
 
-        assert f(2, 1) == g(
-            2
-        )  # they should be in sync, default value should be copied.
-        assert f(2, 1) == g(
-            2
-        )  # they should be in sync, default value should be copied.
-        f(1, 2)  # put them out of sync
-        assert f(1, 2) != g(1, 2)  # they should not be equal anymore.
+        # Should have been copied because it is mutable
+        assert g.value[s] is not f.value[s]
+
+        # Their contents should be equal, though
+        assert np.array_equal(g.value[s], f.value[s])
+
+        # They should be in sync, default value should be copied
+        assert np.array_equal(f(2, 1), g(2))
+
+        # They should be in sync, default value should be copied
+        assert np.array_equal(f(2, 1), g(2))
+
+        # Put them out of sync
+        f(1, 2)
+
+        # They should not be equal anymore
+        assert not np.array_equal(f(1, 2), g(1, 2))
 
     def test_copy_share_memory(self):
         x = fscalar("x")
@@ -478,9 +486,9 @@ class TestFunction:
             ori = function([x], out, mode=mode, updates={z: z * 2})
             cpy = ori.copy(delete_updates=True)
 
-            assert cpy(1)[0] == 4
-            assert cpy(1)[0] == 4
-            assert cpy(1)[0] == 4
+            assert cpy(1) == 4
+            assert cpy(1) == 4
+            assert cpy(1) == 4
 
         # Test if unused implicit and explicit inputs from delete_updates
         # are ignored as intended.

Copied function does not respect original single output format
```python
import aesara
import aesara.tensor as at

f1 = aesara.function([], at.constant(1.0))
f2 = f1.copy()
print(f1(), f2())  # 1.0 [array(1., dtype=float32)]
```
tests/compile/function/test_types.py::TestFunction::test_copy tests/compile/function/test_types.py::TestFunction::test_copy_delete_updates
tests/compile/function/test_types.py::TestFunction::test_empty tests/compile/function/test_types.py::TestFunction::test_extra_inputs tests/compile/function/test_types.py::TestFunction::test_missing_inputs tests/compile/function/test_types.py::TestFunction::test_input_anon_singleton tests/compile/function/test_types.py::TestFunction::test_input_anon_unpack tests/compile/function/test_types.py::TestFunction::test_naming_rule0 tests/compile/function/test_types.py::TestFunction::test_naming_rule1 tests/compile/function/test_types.py::TestFunction::test_naming_rule2 tests/compile/function/test_types.py::TestFunction::test_naming_rule3 tests/compile/function/test_types.py::TestFunction::test_naming_rule4 tests/compile/function/test_types.py::TestFunction::test_state_access[mode0] tests/compile/function/test_types.py::TestFunction::test_state_access[mode2] tests/compile/function/test_types.py::TestFunction::test_state_access[mode3] tests/compile/function/test_types.py::TestFunction::test_same_names tests/compile/function/test_types.py::TestFunction::test_weird_names tests/compile/function/test_types.py::TestFunction::test_copy_share_memory tests/compile/function/test_types.py::TestFunction::test_swap_SharedVariable tests/compile/function/test_types.py::TestFunction::test_swap_SharedVariable_with_given tests/compile/function/test_types.py::TestFunction::test_shared_state0 tests/compile/function/test_types.py::TestFunction::test_shared_state1 tests/compile/function/test_types.py::TestFunction::test_shared_state2 tests/compile/function/test_types.py::TestFunction::test_shared_state_not_implicit tests/compile/function/test_types.py::TestFunction::test_constant_output tests/compile/function/test_types.py::TestFunction::test_borrow_input tests/compile/function/test_types.py::TestFunction::test_borrow_output tests/compile/function/test_types.py::TestFunction::test_disconnected_input tests/compile/function/test_types.py::TestFunction::test_masked_input tests/compile/function/test_types.py::TestFunction::test_givens_input_var tests/compile/function/test_types.py::TestFunction::test_free tests/compile/function/test_types.py::TestFunction::test_default_values tests/compile/function/test_types.py::TestFunction::test_check_for_aliased_inputs tests/compile/function/test_types.py::TestPicklefunction::test_deepcopy tests/compile/function/test_types.py::TestPicklefunction::test_deepcopy_trust_input tests/compile/function/test_types.py::TestPicklefunction::test_output_keys tests/compile/function/test_types.py::TestPicklefunction::test_deepcopy_shared_container tests/compile/function/test_types.py::TestPicklefunction::test_pickle tests/compile/function/test_types.py::TestPicklefunction::test_multiple_functions tests/compile/function/test_types.py::TestPicklefunction::test_pickle_class_with_functions tests/compile/function/test_types.py::test_empty_givens_updates