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y = 1/x

June 1, 2007 am30 9:56 am

the graph of 1/xWhat a nice way to end the year! My Algebra II/Precalc group, coming off conic sections, were confronted with this. I asked them to create a table, and hand-graph. Lots of reasonably interesting discussion about getting more data points, then about the discontinuity and asymptote (first time they have run into a vertical one), and that horizontal asymptote. We digressed to talk about point discontinuities (eg, y = \frac{x^2 + x}{x+1}), and then I got a moment of satisfaction.

y = \frac{1}{x} + 5. Someone knew it was a vertical shift.

y = \frac{1}{x+2}. Someone guessed it was a horizontal shift. Verified.

y = \frac{10}{x} . Guess: vertical stretch. Verified.

Someone asked about a horizontal stretch. We looked at y = \frac{1}{4x} and y = (\frac{1}{4}) (\frac{1}{x}) to get the relationship.

And then y = \frac{4x + 9}{x+2} didn’t really bother anyone. Someone started dividing right away.

Transforming functions? Taught so much earlier? It sunk in.

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