Question

Bramdy is looking for a function to fit the data points (0,1) (1,2) (2,4.25). So far, she has found four functions that fit the first two data points perfectly. Which of these functions best fits all three data points?

1) y = 2x + 1
2) y = 3x + 1
3) y = 4x + 1
4) y = 5x + 1

Answer 1

None of the given functions perfectly fit all three data points, but the function y = 2x + 1 is the closest match for the third data point.

Step-by-step explanation:

To determine which function best fits the data points (0,1), (1,2), and (2,4.25), we need to plug in the x value of the third point into each function and check which function returns the closest y value to 4.25.

For the first function, y = 2x + 1, plugging in x = 2 gives us y = 2(2) + 1 = 5, which is not close to 4.25.

For the second function, y = 3x + 1, plugging in x = 2 gives us y = 3(2) + 1 = 7, which is further away.

For the third function, y = 4x + 1, plugging in x = 2 gives us y = 4(2) + 1 = 9, even further still.

For the fourth function, y = 5x + 1, plugging in x = 2 gives us y = 5(2) + 1 = 11, which is the furthest from 4.25.

None of these functions perfectly fit the third data point, but the first function, y = 2x + 1, comes closest to the actual y value of 4.25 and therefore would be the best choice from the provided options.

Therefore, the correct option is 1) y = 2x + 1.