for function if the a value 1/2 is it a stretch of 1/2 or a compression of 2. Or is both correct!

If you mean a polynomial such as

a(x-p)(x-q)(x-r)...

then a is the vertical scale value, so a = 1/2 means the y values are half as big: a compression ratio.

stretching and compression are just two ways of looking at a scale factor. Usually a compression means a < 1 and a stretch means a > 1, but that's just interpretation.

To determine whether the given function has a stretch or compression, we need to examine the coefficient in front of the variable. In this case, the coefficient is 1/2.

If the coefficient is greater than 1, it represents a stretch of the graph. This means that the graph will be stretched vertically. The larger the coefficient, the greater the stretch.

If the coefficient is between 0 and 1, it represents a compression of the graph. This means that the graph will be compressed vertically. The smaller the coefficient, the greater the compression.

In this case, since the coefficient is 1/2, it is between 0 and 1. Therefore, we can say that it represents a compression. However, the coefficient can also be thought of as the reciprocal of the stretch factor. If we take the reciprocal of 1/2, we get 2, which is greater than 1. Hence, it can also be interpreted as a stretch of 1/2.

Both interpretations are correct, but they highlight different perspectives. We can say that the graph is compressed by a factor of 1/2 or stretched by a factor of 2.