1. The problem is to analyze and graph the function $$y=\left(\frac{1}{4}\right)^{-x} - 5$$. 2. Recall the rule for negative exponents: $$a^{-x} = \frac{1}{a^x}$$. Applying this to $$\left(\frac{1}{4}\right)^{-x}$$ gives: $$\left(\frac{1}{4}\right)^{-x} = 4^x$$. 3. So the function simplifies to: $$y = 4^x - 5$$. 4. This is an exponential function with base 4, shifted down by 5 units. 5. Key features: - The horizontal asymptote is at $$y = -5$$. - The y-intercept is at $$x=0$$, so $$y = 4^0 - 5 = 1 - 5 = -4$$. - As $$x \to \infty$$, $$y \to \infty$$. - As $$x \to -\infty$$, $$y \to -5$$ from above. 6. The graph is an increasing exponential curve shifted down by 5. Final answer: $$y = 4^x - 5$$