Concept Byte: Graphing Rational Functions

Use With Lesson 11-7

TECHNOLOGY

Functions such as y = 1 x , y = 1 x + 2 , y equals , 1 over x . comma . y equals . fraction 1 , over x plus 2 end fraction . comma  and y = 1 x − 4 y equals , 1 over x , minus 4  are examples of rational functions. When you use a graphing calculator to graph a rational function, false connections may appear on the screen. When this happens, you need to make adjustments to see the true shape of the graph.

Graph the function y = 1 x + 2 − 4 . y equals . fraction 1 , over x plus 2 end fraction . minus 4 . .  You can enter this as y = 1 ÷ ( x + 2 ) − 4 . y equals 1 divides open x plus 2 close minus 4 .  The graph on your screen may look like the one below. The highest point and the lowest point on the graph that appear on the screen are not supposed to connect. If you use the trace begin box , trace , end box  key on the calculator, you can see that no point on the graph lies on this connecting line. So this is a false connection.

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Here's how you can graph a rational function and avoid false connections.

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

  

• Step 2 Graph the y = 1 x + 2 − 4 y equals . fraction 1 , over x plus 2 end fraction . minus 4  again. Now the false connection is gone.

  

• Step 3 Use the trace begin box , trace , end box  key or TABLE feature to find some points on the graph. Sketch the graph.

  
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Exercises

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

1. y = 3 x y equals , 3 over x
2. y = − 4 x y equals negative , 4 over x
3. y = 1 x + 2 y equals . fraction 1 , over x plus 2 end fraction
4. y = 1 x − 4 y equals . fraction 1 , over x minus 4 end fraction
5. y = 1 x + 2 y equals , 1 over x , plus 2
6. y = 1 x − 3 y equals , 1 over x , minus 3
7. y = 1 x − 1 + 2 y equals . fraction 1 , over x minus 1 end fraction . plus 2
8. y = 3 x − 2 − 4 y equals . fraction 3 , over x minus 2 end fraction . minus 4
9. 1. Graph y = 1 x , y = 1 x − 4 , y equals , 1 over x . comma . y equals . fraction 1 , over x minus 4 end fraction . comma  and y = 1 x + 3 . y equals . fraction 1 , over x plus 3 end fraction . .
   2. Make a Conjecture How does adding or subtracting a positive number in the denominator of y = 1 x y equals , 1 over x  translate the graph?
10. 1. Graph y = 1 x , y = 1 x − 4 , y equals , 1 over x . comma . y equals , 1 over x , minus 4 . comma  and y = 1 x + 3 . y equals , 1 over x , plus 3 . .
    2. Make a Conjecture How does adding or subtracting a positive number on the right side of y = 1 x y equals , 1 over x  translate the graph?

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