This should have been posted in the Pre-Calculus subforum.
Let's compare to . The latter is a horizontal stretch by a factor of 2. The minimum and maximum y values, if any, do not change. The maximum value of the latter function would still be y = 6.
(Look at a concrete example: and . In both cases, the minimum and maximum values are -1 and 1, respectively.)
Okay, now let's compare to . This time, the latter has a vertical shrink by a factor of 1/3. The minimum and maximum y values, if any, this time, will change. The maximum value of the latter function is now y = 2 (just multiply 6 by 1/3).
(Look at another concrete example: vs. . The min & max values for the original function are -1 and 1, but the min & max values for the transformed function are -1/3 and 1/3.)
Does that help?