The table shows a function. Is the function linear or nonlinear?
x y
–2 18
–1 13
0 9
To determine if a function is linear or nonlinear, we need to check if there is a constant rate of change between the x and y values.
Let's calculate the rate of change between the given points:
For the first two points:
Rate of change = (y2 - y1) / (x2 - x1)
= (13 - 18) / (-1 - (-2))
= (-5) / (1)
= -5
Now, let's calculate the rate of change between the second two points:
Rate of change = (y2 - y1) / (x2 - x1)
= (9 - 13) / (0 - (-1))
= (-4) / (1)
= -4
Since the rate of change is not constant between all pairs of points, the function is nonlinear.