The table shows a function. Is the function linear or nonlinear?
x y
–10 19
–5 15
0 –10
To determine if the function is linear or nonlinear, we can examine the relationship between the x-values and y-values.
In a linear function, the change in y-values is constant for each unit change in x-values. This means that the ratio of the change in y to the change in x is always the same.
Let's calculate the change in y for each unit change in x:
From x = -10 to x = -5:
Change in y = 15 - 19 = -4
From x = -5 to x = 0:
Change in y = -10 - 15 = -25
The difference in y-values is not constant for each unit change in x, which means the function is nonlinear.
To determine if the function is linear or nonlinear, we can see if there is a constant rate of change between the x and y values.
Let's calculate the rate of change between the x and y values:
From (-10, 19) to (-5, 15):
Rate of change = (15 - 19) / (-5 - (-10)) = -4 / 5 = -0.8
From (-5, 15) to (0, -10):
Rate of change = (-10 - 15) / (0 - (-5)) = -25 / 5 = -5
As we can see, the rate of change is not constant. It changes from -0.8 to -5. Since the rate of change is not constant, the function is nonlinear.