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

graph the exponential function.\n\n$f(x)=-2^{-x}$\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$f(x)=-2^{-x}$\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

Rewrite ( -2^{-x} ) as ( -(\frac{1}{2})^x ).

Step2: Identify the horizontal asymptote

As ( x \to \infty ), ( (\frac{1}{2})^x \to 0 ), so the asymptote is ( y = 0 ).

Step3: Calculate five points

  • When ( x = -2 ), ( f(-2) = -(\frac{1}{2})^{-2} = -4 )
  • When ( x = -1 ), ( f(-1) = -(\frac{1}{2})^{-1} = -2 )
  • When ( x = 0 ), ( f(0) = -(\frac{1}{2})^0 = -1 )
  • When ( x = 1 ), ( f(1) = -(\frac{1}{2})^1 = -\frac{1}{2} )
  • When ( x = 2 ), ( f(2) = -(\frac{1}{2})^2 = -\frac{1}{4} )

Answer:

Points: ((-2, -4)), ((-1, -2)), ((0, -1)), ((1, -\frac{1}{2})), ((2, -\frac{1}{4})); Asymptote: ( y = 0 )