$ \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} $

Interactive vertical translations demonstration (in the HTML version only).

Instructions.

Move the slider

Huge thanks to the amazing David Austin for making these interactive javascript graphics for the text.

by clicking and dragging on the red point to see how changing $a$ affects the graph of $y = f(x) + a\text{,}$ which appears in blue. The graph of $y = f(x)$ will appear in grey and remain fixed.