Question

The ordered pairs (1,1), (2,8), (3,27), (4,64) , and (5,125) represent a function. What is a rule that represents this function?

A. y=x
B. y=4x
C. y=x²
D. y=x³

Answer 1

The ordered pairs (1,1), (2,8), (3,27), (4,64), and (5,125) demonstrate a cubic relationship, with each y-value being the cube of the x-value. Hence, the correct rule for this function is D. y = x³.

Step-by-step explanation:

The ordered pairs given are (1,1), (2,8), (3,27), (4,64), and (5,125). To find a rule that represents this function, we need to analyze the relationship between the x and y values of these pairs. If we examine the y-values, we can see that each y is the cube of the corresponding x-value:

• 13 = 1
• 23 = 8
• 33 = 27
• 43 = 64
• 53 = 125

This indicates a direct cubic relationship between each x and y. Therefore, the correct rule for this function is D. y = x³.