It makes it easy to plot functions, check results, and encourages good students to experiment and learn. Personally I found Mathematica extremely useful for learning calculus some 15 years ago (Wolfram|Alpha didn't exist at that time).

I think you definitely should show Wolfram|Alpha to them, and you should take the opportunity to explain why such tools will never be a replacement for mathematical thinking. Stress the importance of learning and present the software in your own context acceptable to the level of the class, and all is well. Tl dr I don't see any trouble or moral issue here. The tools allowed to the students should scale with the familiarity they have with the processes capable of being performed by the tools. In terms of examinations for beginning students however, I tend to agree that at most scientific calculators or similar tools should be allowed. In general, I think given that in advanced classes I still use these softwares to check limiting cases and perform routine calculations with which I'm confident, that becoming familiar with them early on is benign and even important. For learning elementary material I think it is an excellent tool for checking homework to, say, solutions that don't have answers reported or to satisfy curiosities about broader behavior of calculus or certain functions. In particular, I think that the geometric benefits of using Wolfram (Alpha, or Mathematica) are immense. I'm a strong proponent of using computational softwares and engines in elementary courses wherein computation is heavy.

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