Concept Byte: Graphing Rational Functions

For Use With Lesson 8-2

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You can use your graphing calculator to graph rational functions and other members of the reciprocal function family. It is sometimes preferable to use the DOT plotting mode rather than CONNECTED plotting mode. The CONNECTED mode can join branches of a graph that should be separated. Try both modes to get the best graph.

Example

Graph y = 4 x − 3 − 1.5. y equals . fraction 4 , over x minus 3 end fraction . minus , 1.5.

• Step 1 Press the mode begin box , mode , end box  key. Scroll down to highlight the word DOT. Then press enter . begin box , enter , end box , .

  

• Step 2 Enter the function. Use parentheses to enter the denominator accurately.

  

• Step 3 Graph the function.

  
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Exercises

1. 1. Graph the parent reciprocal function y = 1 x . y equals , 1 over x , .
   2. Examine both negative and positive values of x. Describe what happens to the y-values as x approaches zero.
   3. What happens to the y-values as x increases? As x decreases?
2. 1. Change the mode on your calculator to CONNECTED. Graph the function from the example.
   2. Press trace begin box , trace , end box  and trace the function. What happens between x ≈ 2 . 8  and  x ≈ 3 . 2 ? x almost equal to 2 . 8 , and , x almost equal to 3 . 2 question mark
   3. Reasoning How does your graph differ from the graph in the example? Explain the differences.

Use a graphing calculator to graph each function. Then sketch the graph.

3. y = 7 x y equals , 7 over x
4. y = 3 x + 4 − 2 y equals . fraction 3 , over x plus 4 end fraction . minus 2
5. y = x + 2 ( x + 1 ) ( x + 3 ) y equals . fraction x plus 2 , over open , x plus 1 , close . open , x plus 3 , close end fraction
6. y = 4 x + 1 x − 3 y equals . fraction 4 x plus 1 , over x minus 3 end fraction
7. y = 2 x − 2 y equals . fraction 2 , over x minus 2 end fraction
8. y = 1 x + 2 + 3 y equals . fraction 1 , over x plus 2 end fraction . plus 3
9. y = 2 x x + 3 y equals . fraction 2 x , over x plus 3 end fraction
10. y = x 2 x 2 − 5 y equals . fraction x squared , over x squared , minus 5 end fraction
11. y = 20 x 2 + 5 y equals . fraction 20 , over x squared , plus 5 end fraction

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