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

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

Rewrite ( -3^{-x} ) as ( - \left(\frac{1}{3}\right)^x ).

Step2: Identify the horizontal asymptote

As ( x \to \infty ), ( \left(\frac{1}{3}\right)^x \to 0 ), so the asymptote is ( y = 0 ).

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

  • ( x = -2 ): ( f(-2) = - \left(\frac{1}{3}\right)^{-2} = -9 )
  • ( x = -1 ): ( f(-1) = - \left(\frac{1}{3}\right)^{-1} = -3 )
  • ( x = 0 ): ( f(0) = - \left(\frac{1}{3}\right)^0 = -1 )
  • ( x = 1 ): ( f(1) = - \left(\frac{1}{3}\right)^1 = -\frac{1}{3} )
  • ( x = 2 ): ( f(2) = - \left(\frac{1}{3}\right)^2 = -\frac{1}{9} )

Step4: Plot the points and asymptote

Points: ((-2, -9)), ((-1, -3)), ((0, -1)), ((1, -\frac{1}{3})), ((2, -\frac{1}{9})). Asymptote: ( y = 0 ) (x-axis).

Answer:

Five points: ((-2, -9)), ((-1, -3)), ((0, -1)), ((1, -\frac{1}{3})), ((2, -\frac{1}{9})). Asymptote: ( y = 0 ). The graph approaches ( y = 0 ) as ( x \to \infty ) and decreases rapidly as ( x \to -\infty ).