graph the function (f(x)=-4^{x - 5}+5) on the axes below. you must plot the asymptote and any two points…

Explanation:

Step1: Find the horizontal asymptote

For an exponential - type function of the form (y = a\cdot b^{x - h}+k), the horizontal asymptote is (y = k). In the function (f(x)=-4^{x - 5}+5), (a=-1), (b = 4), (h = 5), and (k = 5). So the horizontal asymptote is (y = 5).

Step2: Find the first point

Let (x = 5). Then (f(5)=-4^{5 - 5}+5=-4^{0}+5=-1 + 5=4). So the point is ((5,4)).

Step3: Find the second point

Let (x = 6). Then (f(6)=-4^{6 - 5}+5=-4^{1}+5=-4 + 5 = 1). So the point is ((6,1)).

Answer:

Asymptote: (y = 5) Points: ((5,4)) and ((6,1))