Too Old for This?

I was going over a written assignment: “Using a calculator, graph f(x)=(x-1)(x-2) and g(x) = |(x-1)(x-2)|.  Describe and explain the difference.”  Several students said there was no difference and produced these graphs copied from their calculators.

Graphs From Afar

Graphs From Afar

To demonstrate the error of their ways, I stated that Rock Hudson and I look the same from a distance (a very far distance) but, when you zoom in, we are different.  What?!  How would they know anything about Rock Hudson, a  1950’s movie star. So I changed it to Brad Pitt who probably is still just some old man to them.  I went back to my point:  different functions (algebraically)  => different graphs. So look closely and explain the difference: particular character of the function expression (in this case, absolute value) => particular look of the graph (in this case, all on or above the x-axis, negative values reflected about the x-axis.)

Graphs Closer

Graphs Closer

I will be introducing the standard equation of a circle today asking, “What is a circle?” Usually some student will say it is round.   I hope I can refrain from singing, “Round thing, you make my heart sing, ” with the appropriate phrasing and a slight twang.  I think I have become quaint.


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.
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