diff --git a/lib/matplotlib/axes/_secondary_axes.py b/lib/matplotlib/axes/_secondary_axes.py
@@ -6,6 +6,7 @@
 import matplotlib.ticker as mticker
 from matplotlib.axes._base import _AxesBase, _TransformedBoundsLocator
 from matplotlib.axis import Axis
+from matplotlib.transforms import Transform
 
 
 class SecondaryAxis(_AxesBase):
@@ -144,11 +145,17 @@ def set_functions(self, functions):
             If a transform is supplied, then the transform must have an
             inverse.
         """
+
         if (isinstance(functions, tuple) and len(functions) == 2 and
                 callable(functions[0]) and callable(functions[1])):
             # make an arbitrary convert from a two-tuple of functions
             # forward and inverse.
             self._functions = functions
+        elif isinstance(functions, Transform):
+            self._functions = (
+                 functions.transform,
+                 lambda x: functions.inverted().transform(x)
+            )
         elif functions is None:
             self._functions = (lambda x: x, lambda x: x)
         else:

diff --git a/lib/matplotlib/tests/baseline_images/test_axes/secondary_xy.png b/lib/matplotlib/tests/baseline_images/test_axes/secondary_xy.png
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
@@ -7494,6 +7494,20 @@ def test_annotate_across_transforms():
                 arrowprops=dict(arrowstyle="->"))
 
 
+class _Translation(mtransforms.Transform):
+    input_dims = 1
+    output_dims = 1
+
+    def __init__(self, dx):
+        self.dx = dx
+
+    def transform(self, values):
+        return values + self.dx
+
+    def inverted(self):
+        return _Translation(-self.dx)
+
+
 @image_comparison(['secondary_xy.png'], style='mpl20')
 def test_secondary_xy():
     fig, axs = plt.subplots(1, 2, figsize=(10, 5), constrained_layout=True)
@@ -7513,6 +7527,7 @@ def invert(x):
         secax(0.4, functions=(lambda x: 2 * x, lambda x: x / 2))
         secax(0.6, functions=(lambda x: x**2, lambda x: x**(1/2)))
         secax(0.8)
+        secax("top" if nn == 0 else "right", functions=_Translation(2))
 
 
 def test_secondary_fail():