In algebra, equations can be stretched horizontally or vertically along an axis by multiplying either x or y by a number, respectively. By multiplying f(x) by a number greater than one, all the y values of an equation increase. This leads to a "stretched" appearance in the vertical direction. If f(x) is multiplied by a value less than one, all the y values of the equation decrease, leading to a "shrunken" appearance in the vertical direction. Alternatively, if only x is multiplied, the graph stretches or shrinks in the horizontal direction.
For examples, we will use the basic trignometric function f(x) = sin(x), which is black in the two graphs in Figure 1. Stretches can be a bit confusing with linear or quadratic functions, but they are much more straight forward with the sine function. The red function in Figure 1 has been stretched (dilated) vertically by a factor of 3 and follows the equation:
In general a vertical stretch is given by the equation:
If p is larger than 1, the function gets "taller." If p is smaller than 1, the function gets "shorter."
The blue function in Figure 2 has been been stretched horizontally by a factor of 3 and has the equation:
In general, a horizontal stretch is given by the equation:
In the example above, q = 1/3. When q is larger than 1, the function will get "longer" and when q is smaller than 1, the function will "squish".