Algebra.Com's Answer #403507 by Edwin McCravy(20081)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
If I was given a graph of y=f(x) and the graph has points: (-4,0), (0,2), (2,-2), (3,0) connected in that order. How would I sketch the graph of y = f(x-1)?
\n" );
document.write( "----------\r\n" );
document.write( "\r\n" );
document.write( "If you had, say this graph:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "f(x-1) means that you are subtracting 1 from the value of the variable,\r\n" );
document.write( "therefore you must choose x as 1 GREATER to compensate for the 1 that\r\n" );
document.write( "is subtracted from the variable. This may seem confusing, but if you\r\n" );
document.write( "think about it, when you subtract from the variable, you must choose a \r\n" );
document.write( "larger value of x that will overcome the subtraction. Therefore you would \r\n" );
document.write( "add 1 to each x-coordinate and shift each point to the right by 1 unit and \r\n" );
document.write( "the new points would be (-3,0), (1,2), (3,-2), (4,0). \r\n" );
document.write( "\r\n" );
document.write( "A larger value of x must be chosen to produce the same value of y that x\r\n" );
document.write( "would have produce if 1 had not been subtracted from the variable x. \r\n" );
document.write( " \r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "-----------\r\n" );
document.write( "\r\n" );
document.write( "What about y=|f(x)|?\r\n" );
document.write( "\r\n" );
document.write( "The absolute value never becomes negative, and so any part of the graph \r\n" );
document.write( "that drops below the x-axis must be reflected above the x axis. That\r\n" );
document.write( "means change any negative y-coordinates to positive. The points with\r\n" );
document.write( "positive y-coordinates will not change. So the points will be \r\n" );
document.write( "(-4,0), (0,2), (2,2), (3,0). All the poins above the x-axis will be the\r\n" );
document.write( "same and in this case only the one point (2,-2) has a negative y value,\r\n" );
document.write( "and so the others are the same and only (2,-2) changes to (2,2). Notice \r\n" );
document.write( "below that the portion of the original graph that contains (2,-2) got \r\n" );
document.write( "reflected across the x-axis, and the rest of the graph is the same as\r\n" );
document.write( "the original. If the original graph goes down below the x-axis to the\r\n" );
document.write( "left of (-2,0), as this one does, then that part will be reflected above \r\n" );
document.write( "the x-axis. IOW the part of the graph that falls below the x-axis will\r\n" );
document.write( "be reflected above the x-axis. \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "What about y=f|x|?\r\n" );
document.write( "\r\n" );
document.write( "This will ignore anything on the left of the y-axis in the original graph,\r\n" );
document.write( "since all negative values of x become positive, and so it amounts to not \r\n" );
document.write( "substituting any negative values of x in the original equation f(x), then\r\n" );
document.write( "refecting what's on the right of the y-axis into the y-axis. Note that \r\n" );
document.write( "the point(-4,0) is not used or reflected at all because it cannot be a value \r\n" );
document.write( "of |x| to produce any value for f(|x|) at all. Also notice that (2,-2)\r\n" );
document.write( "reflects across the y-axis into the point (-2,-2). The point that is on\r\n" );
document.write( "the y-axis (0,2) reflects into itself, just as points on a mirror reflect\r\n" );
document.write( "into themselves. \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Edwin \n" );
document.write( " |