Question

What is the rule for the function represented by the following ordered pairs? DO NOT USE DECIMALS-LEAVE AS FRACTIONS. (O, 7/8), (1,2), (2, 25/8), (3, 17/4), (4, 43/8)?

A) f(x) = x + 7/8
B) f(x) = 2x - 1
C) f(x) = 3x - 1/8
D) f(x) = (5/2)x - 1/2.

Answer 1

The rule for the function represented by the given ordered pairs is f(x) = (3/4)x + 7/8.

Step-by-step explanation:

To find the rule for the function represented by the given ordered pairs, we need to look for a pattern or relationship between the x-values and the corresponding y-values. Let's examine the differences between consecutive x-values and the corresponding y-values:

1. The difference between 1 and 0 is 1, and the difference between 2 and 1 is also 1. The difference between the corresponding y-values (2 and 7/8) is 2 - 7/8 = 9/8.
2. The difference between 2 and 1 is 1, and the difference between 3 and 2 is also 1. The difference between the corresponding y-values (25/8 and 2) is 25/8 - 2 = 9/8.
3. The difference between 3 and 2 is 1, and the difference between 4 and 3 is also 1. The difference between the corresponding y-values (17/4 and 25/8) is 17/4 - 25/8 = 3/8.

Since the differences between the x-values are 1 and the differences between the y-values are constant (9/8 and 3/8), we can conclude that the rule for the function is linear, and the common difference for the y-values is 9/8 - 3/8 = 6/8 = 3/4. Therefore, the rule for the function is

f(x) = (3/4)x + 7/8.