is this function linear, quadratic, or exponential?

Explanation:

Step1: Calculate the change in (x) and (y)

The change in (x) ((\Delta x)): (-4-(-5)=1), (-3 - (-4)=1), (-2-(-3)=1), (-1-(-2)=1) (constant (\Delta x = 1)). The change in (y) ((\Delta y)): (14 - 20=-6), (8 - 14=-6), (2 - 8=-6), (-4 - 2=-6) (constant (\Delta y=-6)).

Step2: Check the type of function

For a linear function, if the change in (x) ((\Delta x)) is constant and the change in (y) ((\Delta y)) is also constant, the function is linear. Here, since (\Delta x) is constant ((1)) and (\Delta y) is constant ((-6)), the function follows the form (y=mx + b) (where (m=\frac{\Delta y}{\Delta x}=-6)).

For a quadratic function (y = ax^{2}+bx + c), the second - order differences of (y) (when (x) has a constant first - order difference) would be constant. But we have a constant first - order difference of (y).

For an exponential function (y = a\cdot b^{x}), the ratio of (y) - values ((\frac{y_{n + 1}}{y_{n}})) would be constant when (x) has a constant difference. Here, (\frac{14}{20}=0.7), (\frac{8}{14}\approx0.57), so the ratio is not constant.

Answer:

linear