When I introduce the concept of function in my college algebra class, I emphasize that the formula is not enough. To really know a function is to know its formula and its shape (graph) and its domain and range and its important points including zeros, y-intercept, minima and maxima, and its behavior when x is very large or small and its vertical asymptotes if any. I was casting about for a problem for a high school math contest and came up with this.

Graph

The correct answer would be a horizontal line at with holes at and . I didn’t use the problem but I decided to test *Wolfram Alpha* which I know has problems along this line.

Wolfram Alpha Example 1

This query gave a wrong or at least a insufficient answer.

I guess *Wolfram* *Alpha*‘s has a different idea about what is important information about a function and its graph. I also tried this query.

Wolfram Alpha Example 2

Essentially the same incomplete answer.

Finally I tried, as Nick Chura has suggested, asking directly about the domain and got the correct answer.

Wolfram Alpha Example 3

So *Wolfram Alpha *has the tools but not the philosophy.

By the way, this is a cool technique for putting holes in function graphs. If you want a hole at say just multiply the function formula by . So has a hole at . I particularly like this function . The vertex point is removed and the function is now differentiable in its entire domain. It is a satisfying exercise to calculate its derivative.

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## About jrh794

I am a sixty-five year old math instructor at Southern Oregon University. I taught at the College of the Siskiyous in Weed California for twenty-six years. Prior to that I worked as a computer programmer, carpenter and in various other jobs. I graduated from Rice University in 1967 and have a MS in Operations Research from Stanford. In the past I have hand-built a stone house and taken long solo bicycle tours. Now I ride my mountain bike and play golf for recreation.