Question

Write a function rule relating x and y.
a. (1,1/2), (2,2), (3,4 1/2), (4,8)​, (5,12 1/2)

Answer 1

The function rule relating x and y for the given points is y = (1/2)x^2. Each point validates this rule, with y equal to half of x squared.

Step-by-step explanation:

To write a function rule relating x and y for the given points (1,1/2), (2,2), (3,4 1/2), (4,8), and (5,12 1/2), we should look for a pattern in how x changes with respect to y. After inspecting the given points, we notice that as x increases by 1, y seems to increase by successive odd numbers starting at 1 and a half (3/2). Specifically, for each x, y equals (1/2)x2. To verify, we can check this pattern for each point:

• If x = 1, y = (1/2)(1)2 = 1/2, which matches our first point.
• If x = 2, y = (1/2)(2)2 = 2, matching our second point.
• If x = 3, y = (1/2)(3)2 = 9/2 or 4 1/2, matching the third point.
• If x = 4, y = (1/2)(4)2 = 8, matching the fourth point.
• If x = 5, y = (1/2)(5)2 = 25/2 or 12 1/2, matching the fifth point.

Therefore, the function rule that relates x and y is y = (1/2)x2.