graph the exponential function.\n\n$f(x)=-2^{x}$\n\nplot five points on the graph of the function, and also…

Explanation:

Step1: Choose x - values

Let (x=- 2,-1,0,1,2).

Step2: Calculate corresponding y - values for (x = - 2)

Substitute (x=-2) into (y = - 2^{x}), we get (y=-2^{-2}=-\frac{1}{4}=-0.25).

Step3: Calculate corresponding y - values for (x=-1)

Substitute (x = - 1) into (y=-2^{x}), we get (y=-2^{-1}=-\frac{1}{2}=-0.5).

Step4: Calculate corresponding y - values for (x = 0)

Substitute (x = 0) into (y=-2^{x}), we get (y=-2^{0}=-1).

Step5: Calculate corresponding y - values for (x = 1)

Substitute (x = 1) into (y=-2^{x}), we get (y=-2^{1}=-2).

Step6: Calculate corresponding y - values for (x = 2)

Substitute (x = 2) into (y=-2^{x}), we get (y=-2^{2}=-4). The five points are ((-2,-0.25),(-1, - 0.5),(0,-1),(1,-2),(2,-4)). For the exponential function (y=-2^{x}), the horizontal asymptote is (y = 0) (as (x\to\infty), (y\to-\infty) and as (x\to-\infty), (y\to0) from the negative - side).

Answer:

The five points are ((-2,-0.25),(-1,-0.5),(0,-1),(1,-2),(2,-4)) and the horizontal asymptote is (y = 0).