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The stretches you have seen so far have been the simplest cases—stretching the function about either the xaxis or the yaxis. Functions can be stretched about other lines as well.
Before computers were used to graph equations, these kinds of stretches were drawn by hand using a couple of simple ideas. To draw a vertical stretch by hand, you first measure the distance from the line to the graph. Then you multiply this distance by the stretch factor and plot the new point the calculated distance from the line. Repeat these steps until the new graph is complete. Horizontal stretches can be drawn in a similar manner.
Example 1 Examine the following graphs. Here, the graph of y = g(x) is the graph of y = f(x) stretched vertically by a factor of 2 about the line y = 5. Notice that all points on the line y = 5 are invariant (unchanged) under this transformation. Also, notice that the vertex has moved to twice the distance from the line y = 5. The vertex of f(x), (1,3), is 2 units from y = 5; and the vertex of g(x), (1, 1), is 4 units from y = 5. 
Example 2 xamine the following graphs. Here the graph of y = k(x) is the graph of y = h(x) stretched by a factor of about the line x = 3. Notice that the points on the line x = 3 are invariant under this transformation. Also, notice that the vertex of k(x) is 1/3 the distance from x = 3 compared to the distance of the vertex of h(x). The vertex of y = h(x), (3,3), is 6 units from x = 3; and the vertex of k(x), (1, 3), is 2 units from x = 3. 
Example 3 The graph of is stretched by a factor of 2 about the line y = 5.
Solution

Parts of this work has been adapted from a Math 30 Pure learning resource originally produced and owned by Alberta Education