The table shows a function. Is the function linear or nonlinear?
x y
–3 5
12 2
17 –4
To determine if the function is linear or nonlinear, we can check if there is a constant rate of change between the x and y values.
Using the first two points: (-3, 5) and (12, 2), we can calculate the rate of change.
y2 - y1 / x2 - x1 = (2 - 5) / (12 - (-3))
= -3 / 15
= -1/5
Using the second and third points: (12, 2) and (17, -4), we can again calculate the rate of change.
y2 - y1 / x2 - x1 = (-4 - 2) / (17 - 12)
= -6 / 5
= -6/5
Since the rate of change is not consistent and is different between the two sets of points, the function is nonlinear.
To determine whether the function is linear or nonlinear, we need to check if the rate of change between the x-values and y-values remains constant.
Using the given table, let's calculate the rate of change between the first two points and then between the second and third points:
For the first two points (-3, 5) and (12, 2), the rate of change is:
(2 - 5) / (12 - (-3)) = -3 / 15 = -1/5.
Now let's calculate the rate of change between the second and third points (12, 2) and (17, -4):
(-4 - 2) / (17 - 12) = -6 / 5 = -6/5.
Since the rate of change is not constant, the function is nonlinear.