by T. Ford - Email me if you find any errors.
Simply:
| Step 1: Pick Function Graph |
Step 2: Choose an Action |
Generic Formula Adjustment |
 |
Reflect on X axis Reflect on Y axis Shift left Shift right Shift up Shift down Shrink vertically Stretch vertically Shrink horizontally Stretch horizontally |
y=-f(x) y=f(-x) y=f(x+b) y=f(x-b) y=f(x)+b y=f(x)-b y=af(x), 0<a<1 y=af(x), a>1 y=f(cx), c>1 y=f(cx), 0<c<1 |
| Step 3: Squish. See below. | ||
Using the above, variations on functions can be split apart. Example 1: y = -a|-cx + b| + d Graph: y = |x| Reflect on x axis. (first - sign) (make it upside down!) If a>1, stretch vertically. If a<1, shrink vertically. Reflect on the y axis. (second - sign) (note: no change for absolute value graph) If c>1, shrink horizontally. If c<1, stretch horizontally. Shift it left b. (for the + b inside the absolute value function) Shift it up d. (for the + d outside the absolute value function) Example 2: y = -a(1/(cx - b)) + d Graph: y = 1/x Reflect on x axis. (first - sign) (make it upside down!) If a>1, stretch vertically. If a<1, shrink vertically. Do not reflect on the y axis. (missing - sign on c) If c>1, shrink horizontally. If c<1, stretch horizontally. Shift it right b. (for the - b inside the absolute value function) Shift it up d. (for the + d outside the absolute value function) Example 3: y = -(1/2)x - 1 Graph y=x Reflect on x axis. (first - sign) (make it upside down!) Shrink vertically. ((1/2)<1) No modifications to x, so no y axis reflection, horizontal stretching, or horizontal shifting. A modification to x might look like: y = -(1/2)(2x+3) - 1 Shift it down 1. (for the - 1 outside the linear function)
