Stretching and Shrinking Translations
Objective: The learner will be able to state what part of the exponential function determines stretching or shrinking.
Objective: Given an exponential function the learner will state whether the function has been stretched or shrunk and by how much?
Positive Stretch
If you examine closely any xvalue on these two graphs you will notice that the stretched function's yvalue is always 3 times further above the xaxis then the original function. For example (0, 1) is a point on the original graph, while (0,3) is the point on the stretched function. 
Positive Shrink
In this function you will notice that the shrunk function is only 1/4 as high as the original function at each value of x. For example, at x = 2, the original function has a value of 8. While the shrunk function has a value of 2. The points are (2,8) and (2, 2), respectively.


Negative Stretch
When the stretch value c < 1 it has two effects upon the original graph. First, the graph is reflected through the xaxis. Second, the original graph is stretched by c. In the above example the stretched graph is going down, and at any xvalue that you pick along the xaxis you will see that the stretched function's yvalue is twice as far away from the xaxis then the original function. For example: (0, 1), and (1, 2) are on the original function, while (0, 2), and (1, 4) are on the negatively stretched function. In general, the point (x, 2^x) becomes (x, 2 * 2^x).

Negative Shrink
When the stretch value c satisfies 1 < c < 0, it again has two effects upon the original graph. First, because c is negative, the graph is reflected through the xaxis. Second, the original graph is shrunk by c. In the above example the shrink factor is 1/5. The point (0, 1) on the original becomes (0, 0.2), and the point (1, 2) becomes (1, 2/5). In general, the point (x, 2^x) becomes (x, 1/5 * 2^x). 

Positive Stretch  Table
Negative Stretch If 3 is replaced with 3, we would then have a negative stretch. All the values in the third column would be negative. 
Positive Shrink  Table
In the table above notice that all the values in column 3 are half of those in column 2. The second function multiplies each yvalue by 1/2. If Negative Shrink If 1/2 were replaced by 1/2, we would then have a negative shrink. All the values in the third column would be negative. 

Practice Stretch and Shrink Translations
Suggested Practice: Make sure the NoGrid/Grid is set to Grid. Enter a value for c. Then predict where the stretch or shrink graph will be drawn. Then click on Graph and see if you are correct.

