Summary of Graphing Techniques (Transformations)

SUMMARY OF GRAPHING TECHNIQUES (TRANSFORMATIONS)

Equation How to obtain the graph from that of y = f(x)

1) y = f (x) + c, c>0 Raise the graph of f by c units.

2) y = f (x) – c, c>0 Lower the graph of f by c units.

3) y = f (x + c), c>0 Shift the graph of f to the left c units.

4) y = f (x – c), c>0 Shift the graph of f to the right c units.

5) y = cf (x), c>1 Stretch the graph of f vertically away from the x-axis by a factor of c.

6) y = cf (x), 0

7) y = f (cx), 0

8) y = f (cx), c>1 Compress the graph of f horizontally towards the y-axis by a factor of c.

9) y = -f (x) Reflect the graph of f about the x-axis.

10) y = f (-x) Reflect the graph of f about the y-axis.