Translations and Reflections of Graphs – A13

About the lecture

In this mini-lecture, we cover Topic A13 by considering translations and reflections of graphs. As we move through this mini-lecture, we consider: (i) how adding to or subtracting from y translates the function up or down, respectively — this corresponds to vertical translations; (ii) how replacing x by x – 1 translates the graph to the right one unit and replacing x by x + 1 shifts the graph to the left one unit; (iii) how this rule, which might seem counterintuitive when compared to the rule for vertical translations, is actually closely related to the vertical translation rule; (iv) how we can use the techniques of completing the square to better understand horizontal translations; (v) the cosine graph, which is the sine graph shift 90º to the left; (vi) reflecting graphs horizontally, which is done by replacing y with -y; (vii) reflecting graphs vertically, which is done by replacing x with -x; and (viii) an exercise for students to try on their own.

About the lecturer

Keith Ball is a Professor of Mathematics and the University of Warwick. His research interests are in functional analysis, high-dimensional and discrete geometry, and information theory. From 2010-14, Professor Ball served as the scientific director of the International Centre for Mathematical Sciences (ICMS) based in Edinburgh. He was elected as a Fellow of the Royal Society in 2013 and awarded the Whitehead Prize by the London Mathematical Society in 1992. Professor Ball is the author of Strange Curves, Counting Rabbits, and other Mathematical Explorations (2006), a recreational maths book aimed at those familiar with basic calculus.