Problem 3 Writing a Rule to Describe a Nonlinear Function

The ordered pairs (1, 2), (2, 4), (3, 8), (4, 16), and (5, 32) represent a function. What is a rule that represents this function?

Make a table to organize the x- and y-values. For each row, identify rules that produce the given y-value when you substitute the x-value. Look for a pattern in the y-values.

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The function can be represented by the rule y = 2 x . y equals 2 x .

✓ Got It?

3. What is a rule for the function represented by the ordered pairs (1, 1), (2, 4), (3, 9), (4, 16), and (5, 25)?

✓ Lesson Check

Do you know HOW?

1. Graph the function represented by the table below. Is the function linear or nonlinear?

   x	0	1	2	3	4
   y	12	13	14	15	16

2. The ordered pairs ( 0 , − 2 ) , open 0 comma negative 2 close comma  (1, 1), (2, 4), (3, 7), and (4, 10) represent a function. What is a rule that represents this function?

3. Which rule could represent the function shown by the table below?

   x	0	1	2	3	4
   y	0	− 1 negative 1	− 4 negative 4	− 9 negative 9	− 16 negative 16

   1. y = x 2 y equals , x squared
   2. y = − x 3 y equals negative , x cubed
   3. y = − x 2 y equals negative , x squared

Do you UNDERSTAND?

4. Vocabulary Does the graph represent a linear function or a nonlinear function? Explain.

   1. 
   2. 
5. Error Analysis A classmate says that the function shown by the table below can be represented by the rule y = x + 1 . y equals x plus 1 .  Describe and correct your classmate's error.