Chapter 12 Functions and Graphs

This video contains my full, step‑by‑step explanations of the key ideas from Chapter 12: Functions and Graphs, from Schaum’s College Algebra, 2nd edition. Chapter 12 introduces the foundational language of modern mathematics: variables, relations, and functions, along with the graphical tools used to visualize them. In this video, we explore the essential concepts that allow us to interpret, construct, and transform graphs with confidence. The topics covered include: • Variables and algebraic relations • Definition and interpretation of functions • Function notation and evaluation • The rectangular coordinate system and plotting points • Functions of two variables and their graphs • Symmetry: even, odd, and origin symmetry • Shifts, reflections, and scaling of graphs • How transformations affect the shape and position of a graph • Using a graphing calculator — in this case, Desmos, which did not exist when the book was published, but provides a clean and intuitive way to visualize functions today The goal is to provide rigorous, accessible explanations that help learners understand not only how to graph functions, but how algebraic structure determines the geometry of a graph and how transformations modify it. More chapters and solved problems coming soon. 🎧 Music credit ⭐ Track by nourishedbybmusic: “Study music for focus and Brain power” — available on Pixabay