graph the exponential function.\n\n$f(x)=-\\left(\\frac{1}{2}\\right)^{-x}$\n\nplot five points on the graph…

graph the exponential function.\n\n$f(x)=-\\left(\\frac{1}{2}\\right)^{-x}$\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$f(x)=-\\left(\\frac{1}{2}\\right)^{-x}$\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:

Step 1: Simplify the function

Rewrite (-\left(\frac{1}{2}\right)^{-x}) using exponent rules: (\left(\frac{1}{2}\right)^{-x} = 2^x), so (f(x) = -2^x).

Step 2: Identify the horizontal asymptote

As (x \to \infty), (2^x \to \infty), so (f(x) \to -\infty). As (x \to -\infty), (2^x \to 0), so the horizontal asymptote is (y = 0).

Step 3: Calculate five points

  • For (x = -2): (f(-2) = -2^{-2} = -\frac{1}{4}) → Point: ((-2, -\frac{1}{4}))
  • For (x = -1): (f(-1) = -2^{-1} = -\frac{1}{2}) → Point: ((-1, -\frac{1}{2}))
  • For (x = 0): (f(0) = -2^{0} = -1) → Point: ((0, -1))
  • For (x = 1): (f(1) = -2^{1} = -2) → Point: ((1, -2))
  • For (x = 2): (f(2) = -2^{2} = -4) → Point: ((2, -4))

Answer:

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