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Learning Math Home
Patterns, Functions, and Algebra
 
Session 8 Part A Part B Part C Homework
 
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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

Solution  

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.


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Values like 1/2 and 1/10, -1/2 and -1/10 are interesting to try.   Close Tip

 

Problem B9

Solution  

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

Solution  

Create a graph of this function. What happens as the graph gets near the y-axis? Will it ever cross the y-axis?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
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

Take it Further

Problem B11

Solution  

In the equation (x)(y) = 3, what does the 3 represent, graphically?


Looking back at the Interactive Activity may help.   Close Tip
 

 

Problem B12

write Reflect

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


Take it Further

Problem B13

Solution  

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.

Next > Part C: Different Functions

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