graph the exponential function.\n\n$f(x)=-\\left(\\frac{3}{5}\\right)^{x}$\n\nplot five points on the graph…

graph the exponential function.\n\n$f(x)=-\\left(\\frac{3}{5}\\right)^{x}$\n\nplot five points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.

graph the exponential function.\n\n$f(x)=-\\left(\\frac{3}{5}\\right)^{x}$\n\nplot five points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.

Answer

Explanation:

Step1: Find the y - intercept

Set (x = 0). Then (f(0)=-\left(\frac{3}{5}\right)^0=- 1). So the point is ((0, - 1)).

Step2: Find points for positive x - values

When (x = 1), (f(1)=-\left(\frac{3}{5}\right)^1=-\frac{3}{5}=-0.6). The point is ((1,-0.6)). When (x = 2), (f(2)=-\left(\frac{3}{5}\right)^2=-\frac{9}{25}=-0.36). The point is ((2, - 0.36)).

Step3: Find points for negative x - values

When (x=-1), (f(-1)=-\left(\frac{3}{5}\right)^{-1}=-\frac{5}{3}\approx - 1.67). The point is ((-1,-\frac{5}{3})). When (x = - 2), (f(-2)=-\left(\frac{3}{5}\right)^{-2}=-\frac{25}{9}\approx - 2.78). The point is ((-2,-\frac{25}{9})).

Step4: Determine the asymptote

As (x\to+\infty), (\left(\frac{3}{5}\right)^x\to0), so (y = 0) is the horizontal asymptote.

Answer:

The five points are ((0, - 1)), ((1,-0.6)), ((2, - 0.36)), ((-1,-\frac{5}{3})), ((-2,-\frac{25}{9})) and the horizontal asymptote is (y = 0).