Question

If the points (0, 0), (-1, 1), and (-2, 2) lie on the graph of function h, then which of the following rules could represent the function?

a. h( x) = -2 x
b. h( x) = x2
c. h( x) = | x|
d. None

Answer 1

The correct rule that represents the function is h(x) = x².

Step-by-step explanation:

The given points (0, 0), (-1, 1), and (-2, 2) form a straight line with a positive slope. We can determine the equation of the line using the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

Given the points (-2, 2) and (0, 0), we can find the slope using the formula m = (y2 - y1) / (x2 - x1). Substituting the values, we get m = (0 - 2) / (0 - (-2)) = -1. Since the slope is negative, we can eliminate options (a) and (d).

So, the correct rule that represents the function is h(x) = x² (option b), as it matches the slope of the line formed by the given points.