diff --git a/manimlib/mobject/coordinate_systems.py b/manimlib/mobject/coordinate_systems.py
index 3ebc4377..e97d0ec4 100644
--- a/manimlib/mobject/coordinate_systems.py
+++ b/manimlib/mobject/coordinate_systems.py
@@ -4,8 +4,9 @@ from abc import ABC, abstractmethod
 import numbers
 
 import numpy as np
+import itertools as it
 
-from manimlib.constants import BLACK, BLUE, BLUE_D, GREEN, GREY_A, WHITE, RED
+from manimlib.constants import BLACK, BLUE, BLUE_D, BLUE_E, GREEN, GREY_A, WHITE, RED
 from manimlib.constants import DEGREES, PI
 from manimlib.constants import DL, UL, DOWN, DR, LEFT, ORIGIN, OUT, RIGHT, UP
 from manimlib.constants import FRAME_HEIGHT, FRAME_WIDTH
@@ -18,14 +19,16 @@ from manimlib.mobject.geometry import Line
 from manimlib.mobject.geometry import Rectangle
 from manimlib.mobject.number_line import NumberLine
 from manimlib.mobject.svg.tex_mobject import Tex
-from manimlib.mobject.types.vectorized_mobject import VGroup
 from manimlib.mobject.types.dot_cloud import DotCloud
+from manimlib.mobject.types.surface import ParametricSurface
+from manimlib.mobject.types.vectorized_mobject import VGroup
 from manimlib.utils.config_ops import digest_config
 from manimlib.utils.config_ops import merge_dicts_recursively
 from manimlib.utils.simple_functions import binary_search
 from manimlib.utils.space_ops import angle_of_vector
 from manimlib.utils.space_ops import get_norm
 from manimlib.utils.space_ops import rotate_vector
+from manimlib.utils.space_ops import normalize
 
 from typing import TYPE_CHECKING
 
@@ -234,16 +237,27 @@ class CoordinateSystem(ABC):
         """
         return self.input_to_graph_point(x, graph)
 
-    def bind_graph_to_func(self, graph, func, jagged=False):
+    def bind_graph_to_func(self, graph, func, jagged=False, get_discontinuities=None):
         """
         Use for graphing functions which might change over time, or change with
         conditions
         """
-        graph.x_values = [self.x_axis.p2n(p) for p in graph.get_points()]
-        graph.add_updater(lambda g: g.set_points([self.c2p(x, func(x)) for x in g.x_values]))
-        if jagged:
-            graph.add_updater(lambda g: g.make_jagged())
-        else:
+        x_values = [self.x_axis.p2n(p) for p in graph.get_points()]
+
+        def get_x_values():
+            if get_discontinuities:
+                ds = get_discontinuities()
+                ep = 1e-6
+                added_xs = it.chain(*((d - ep, d + ep) for d in ds))
+                return sorted([*x_values, *added_xs])[:len(x_values)]
+            else:
+                return x_values
+
+        graph.add_updater(lambda g: g.set_points_as_corners([
+            self.c2p(x, func(x))
+            for x in get_x_values()
+        ]))
+        if not jagged:
             graph.add_updater(lambda g: g.make_approximately_smooth())
         return graph