diff --git a/manimlib/mobject/functions.py b/manimlib/mobject/functions.py
index 495b3e67..11e8daf5 100644
--- a/manimlib/mobject/functions.py
+++ b/manimlib/mobject/functions.py
@@ -30,39 +30,17 @@ class ParametricCurve(VMobject):
         return self.t_func(t)
 
     def init_points(self):
-        # TODO, this seems like a mess.
         t_min, t_max, step = self.t_range
-        epsilon = self.epsilon
 
-        discontinuities = filter(
-            lambda t: t_min <= t <= t_max,
-            self.discontinuities
-        )
-        discontinuities = np.array(list(discontinuities))
-        boundary_times = [
-            t_min, t_max,
-            *(discontinuities - epsilon),
-            *(discontinuities + epsilon),
-        ]
+        jumps = np.array(self.discontinuities)
+        jumps = jumps[(jumps > t_min) & (jumps < t_max)]
+        boundary_times = [t_min, t_max, *(jumps - self.epsilon), *(jumps + self.epsilon)]
         boundary_times.sort()
         for t1, t2 in zip(boundary_times[0::2], boundary_times[1::2]):
-            # Get an initial sample of points
-            t_range = list(np.linspace(t1, t2, self.min_samples + 1))
-            samples = np.array([self.t_func(t) for t in t_range])
-
-            # Take more samples based on the distances between them
-            norms = [get_norm(p2 - p1) for p1, p2 in zip(samples, samples[1:])]
-            full_t_range = [t1]
-            for s1, s2, norm in zip(t_range, t_range[1:], norms):
-                n_inserts = int(norm / step)
-                full_t_range += list(np.linspace(s1, s2, n_inserts + 1)[1:])
-
-            points = np.array([self.t_func(t) for t in full_t_range])
-            valid_indices = np.isfinite(points).all(1)
-            points = points[valid_indices]
-            if len(points) > 0:
-                self.start_new_path(points[0])
-                self.add_points_as_corners(points[1:])
+            t_range = [*np.arange(t1, t2, step), t2]
+            points = np.array([self.t_func(t) for t in t_range])
+            self.start_new_path(points[0])
+            self.add_points_as_corners(points[1:])
         self.make_smooth()
         return self
 
@@ -70,7 +48,7 @@ class ParametricCurve(VMobject):
 class FunctionGraph(ParametricCurve):
     CONFIG = {
         "color": YELLOW,
-        "x_range": [-8, 8, 0.5],
+        "x_range": [-8, 8, 0.25],
     }
 
     def __init__(self, function, x_range=None, **kwargs):