Semigroups of transformations and endomorphisms have emerged as powerful algebraic frameworks to elucidate the underlying structures of graphs. By harnessing the principles of semigroup theory, ...

Approaching negative infinity: The graph falls indefinitely as x approaches positive or negative infinity. Approaching a horizontal asymptote: The graph approaches a horizontal line as x approaches ...

Look for Key Features: Identify critical points and characteristics such as intercepts, vertices, asymptotes, and symmetry. Test Points: Choose a few points on the graph and plug their coordinates ...