Students identify horizontal and vertical translations, stretches and compressions, and reflections across the $x$- and $y$-axes, interpreting their effects on equations, graphs, domains, ranges, intercepts, and key points. Students graph and describe combined transformations of familiar parent functions, including linear, quadratic, absolute-value, square-root, and reciprocal functions, using $g(x)=a f(b(x-h))+k$ and the mapping $(x,y)\mapsto\left(\frac{x}{b}+h,ay+k\right)$, with attention to the reciprocal effect of horizontal factors. Students determine transformed equations from graphs by inferring parameters from vertices, intercepts, endpoints, asymptotes, and corresponding points, and connect equations, mappings, tables, and graphical features.