Answer:
f(x) = -5x - 1.
Explanation:
The next value of y is obtained by subtracting 5.
When x = -2, y = 9
when x = -1 , y = 4
when x =0, y = -1.
So the rule will be a linear function of the form y = mx + c where m is the slope and c is the y-intercept (where x = 0).
When x = 0 , y = -1 so c = -1.
The slope of the line = (4-9) / (-1-(-2)) = -5/ 1 = -5.
So the function f(x) = -5x - 1.