Dive into the world of piecewise functions and basic graph translations in this comprehensive lecture. Explore the intricacies of piecewise functions, master the vertical line test, and learn to graph nonlinear functions with confidence. Discover various basic graph shapes and understand how to apply horizontal shifts to transform them. Gain practical experience through student practice sessions, solidifying your understanding of these crucial algebraic concepts. Perfect for intermediate algebra students looking to enhance their mathematical skills and problem-solving abilities.