graph the exponential function.\n\n$f(x)=(\\frac{8}{3})^{-x}$\n\nplot five points on the graph of the…

graph the exponential function.\n\n$f(x)=(\\frac{8}{3})^{-x}$\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$f(x)=(\\frac{8}{3})^{-x}$\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: Simplify the function

$$f(x) = \left( \frac{8}{3} \right)^{-x} = \left( \frac{3}{8} \right)^x$$

Step2: Identify the horizontal asymptote

The horizontal asymptote is (y = 0).

Step3: Calculate points for (x = -2, -1, 0, 1, 2)

  • When (x = -2): (f(-2) = \left( \frac{3}{8} \right)^{-2} = \left( \frac{8}{3} \right)^2 = \frac{64}{9} \approx 7.11)
  • When (x = -1): (f(-1) = \left( \frac{3}{8} \right)^{-1} = \frac{8}{3} \approx 2.67)
  • When (x = 0): (f(0) = \left( \frac{3}{8} \right)^0 = 1)
  • When (x = 1): (f(1) = \frac{3}{8} = 0.375)
  • When (x = 2): (f(2) = \left( \frac{3}{8} \right)^2 = \frac{9}{64} \approx 0.14)

Answer:

Five points: ((-2, \frac{64}{9})), ((-1, \frac{8}{3})), ((0, 1)), ((1, \frac{3}{8})), ((2, \frac{9}{64})); Asymptote: (y = 0)