is this function linear, quadratic, or exponential?\nlinear quadratic exponential

Explanation:

Step1: Check linear function

For a linear function (y = mx + b), the slope (m=\frac{y_2 - y_1}{x_2 - x_1}). (m_1=\frac{-2-(-1)}{1 - 0}=\frac{-2 + 1}{1}=-1), (m_2=\frac{-4-(-2)}{2 - 1}=\frac{-4 + 2}{1}=-2). Since (m_1\neq m_2), it is not linear.

Step2: Check quadratic function

For a quadratic function (y = ax^{2}+bx + c), the second - differences should be constant. First differences: (-2-(-1)=-1), (-4-(-2)=-2), (-8-(-4)=-4), (-16-(-8)=-8). Second differences: (-2-(-1)=-1), (-4-(-2)=-2), (-8-(-4)=-4). Since second differences are not constant, it is not quadratic.

Step3: Check exponential function

For an exponential function (y = ab^{x}), when (x = 0), (y=-1), so (a=-1). When (x = 1), (y=-2=-1\times b^{1}), then (b = 2). Check for (x = 2), (y=-1\times2^{2}=-4); for (x = 3), (y=-1\times2^{3}=-8); for (x = 4), (y=-1\times2^{4}=-16).

Answer:

exponential