<p>SUMMARY OF GRAPHING TECHNIQUES (TRANSFORMATIONS)</p><p>Equation How to obtain the graph from that of y = f(x)</p><p>1) y = f (x) + c, c>0 Raise the graph of f by c units.</p><p>2) y = f (x) – c, c>0 Lower the graph of f by c units.</p><p>3) y = f (x + c), c>0 Shift the graph of f to the left c units.</p><p>4) y = f (x – c), c>0 Shift the graph of f to the right c units.</p><p>5) y = cf (x), c>1 Stretch the graph of f vertically away from the x-axis by a factor of c. </p><p>6) y = cf (x), 0<c< 1 Compress the graph of f vertically towards the x-axis by a factor of c.</p><p>7) y = f (cx), 0<c<1 Stretch the graph of f horizontally away from the y-axis by a factor of c.</p><p>8) y = f (cx), c>1 Compress the graph of f horizontally towards the y-axis by a factor of c.</p><p>9) y = -f (x) Reflect the graph of f about the x-axis.</p><p>10) y = f (-x) Reflect the graph of f about the y-axis.</p>