is this function linear or exponential?\nlinear exponential

Explanation:

Step1: Calculate the change in x and y

The change in (x): (\Delta x=-9-(-10) = 1), (\Delta x=-8 - (-9)=1), etc. (constant change of (1)). The change in (y): (\Delta y=-24-(-27)=3), (\Delta y=-21-(-24) = 3), etc. (constant change of (3)).

Step2: Determine the function type

For a linear function, the rate of change ((\frac{\Delta y}{\Delta x})) is constant. Here, (\frac{\Delta y}{\Delta x}=\frac{3}{1} = 3) (constant). For an exponential function, the ratio of (y)-values for a constant change in (x) is constant. But since (\frac{-24}{-27}\neq\frac{-21}{-24}), it's not exponential.

Answer:

linear