 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum  MENU          Session 8, Part B:
Inverse Proportions

In This Part: Splitting a Prize | Ms. Anwar's Backyard | Another Inverse Porportion

 Consider a new function: (x)(y) = 3. Answer these questions:  Problem B8 Find five negative and five positive x values between -10 and 10. Record them in a table with the corresponding y-values. Be creative! Try some non-integers.  Values like 1/2 and 1/10, -1/2 and -1/10 are interesting to try.   Close Tip Values like 1/2 and 1/10, -1/2 and -1/10 are interesting to try. Problem B9 If x = 0, what happens to y? What happens on a calculator if you ask for the value of y = 3 / x when x = 0? Problem B10 Create a graph of this function. What happens as the graph gets near the y-axis? Will it ever cross the y-axis?  Make sure this graph includes points where x is positive, and other points where x is negative. See Problem B8 if you're unsure what will happen if x = 0.   Close Tip Make sure this graph includes points where x is positive, and other points where x is negative. See Problem B8 if you're unsure what will happen if x = 0.      Problem B11 In the equation (x)(y) = 3, what does the 3 represent, graphically?  Looking back at the Interactive Activity may help.   Close Tip   Problem B12 You've seen two kinds of functions that have similar names: proportion (or direct variation) and inverse proportion (or inverse variation). Compare and contrast these two functions. What does the word "inverse" indicate in this case? Note 7      Problem B13 The equation (x)(y) = 1 is a special kind of inverse variation. How are x and y related in this equation? What does this relationship have to do with solving equations? Problems B8-B10 adapted from IMPACT Mathematics Course 3, developed by Education Development Center, Inc. (New York: Glencoe/McGraw-Hill, 2000), p. 111.   Session 8: Index | Notes | Solutions | Video

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