Vertical Shifts or Translations

<BODY LANG="EN" > <HR><center> <table border=1> <td><A HREF="node47.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="node44.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node49.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node48.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> </table> </center> <HR> <H2>Vertical Shifts or Translations</H2> <P> What is the difference between the functions <IMG WIDTH=62 HEIGHT=14 ALIGN=MIDDLE ALT="y = cos(x)" SRC="img134.gif"> and <IMG WIDTH=91 HEIGHT=22 ALIGN=MIDDLE ALT="y = 5 + cos(x)" SRC="img135.gif">? Let's look at the graphs of these two on the same set of axes. <P> <CENTER> <IMG ALIGN=BOTTOM SRC="plot4.gif" WIDTH=320 HEIGHT=236 ALT="[plot]"> </CENTER> <P> We see that the addition of a constant out in front will cause a vertical <B>translation</B> or vertical shift in the graph. More generally, we can say this: <P> <CENTER> <IMG WIDTH=492 HEIGHT=83 ALIGN=BOTTOM ALT="translation defn" SRC="img136.gif"> </CENTER> <P> Next, we want to shift horizontally. How would this be accomplished? We move to that subject next. <P> <HR><center> <table border=1> <td><A HREF="node47.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="node44.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node49.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node48.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> </table> </center> <HR><P><ADDRESS> <I><A HREF="http://www.math.psu.edu/sellersj/">James A. Sellers</A> </I> </ADDRESS> </BODY>