Real Functions and Graphing Curves — Graphical representation of functions and geometric transformations

About this lesson

This unit introduces polynomial functions (linear, quadratic, and cubic), the absolute value function, and the rational function f(x)=1/x. It explains their basic graphs, domains, ranges, symmetry, and monotonicity. The unit then focuses on geometrical transformations of function curves: vertical translation (y=f(x)+a), horizontal translation (y=f(x+a)), combined translation (y=f(x+a)+b), and reflection on the x-axis (y=-f(x)). Examples and exercises show how to graph transformed functions using standard curves, determine ranges, and investigate monotonicity. The unit also includes piecewise-defined functions and exercises on finding intersection points with axes and symmetry points.