Write a function rule for the table?

x y
-1 -4
0 -3
1 -2
2 -1

1 Answer
May 25, 2018

Answer: y=x3

Explanation:

First, we can see that the function for this table is linear since each time x increases by 1, y also increases by 1. (Note: In general, we can see that a function is linear when the slope m=y2y1x2x1 between each data set is constant.)

Since we have established that the function given is indeed linear, we can use either point-slope form or slope-intercept form to find the function rule. In this case, since we are given a y-intercept (0,3), we will use slope-intercept form: y=mx+b, where m is the slope and b is the y-intercept

Our first step in this process will be finding the slope:
m=y2y1x2x1

Since the function is linear, we can choose any two data points, but choosing a data point in which either x or y is 0 will simplify the calculations. So, we will use (0,3) and (1,2). Plugging into the slope formula:
m=3(2)01=11=1

Since we are given the y-intercept (0,3) we can simply plug b into the slope-intercept form formula and we find the function rule:
y=mx+b

y=1x3

y=x3, which is our final answer