1. **State the problem:** We need to find two points with integer coordinates on the graph of the function $$f(x) = -4^{x+5} + 6$$ and identify the asymptote. 2. **Identify the asymptote:** For exponential functions of the form $$f(x) = a^{x} + k$$, the horizontal asymptote is $$y = k$$. Here, the function is $$f(x) = -4^{x+5} + 6$$, so the horizontal asymptote is $$y = 6$$. 3. **Find two points:** Choose integer values for $$x$$ and calculate $$f(x)$$. - For $$x = -5$$: $$f(-5) = -4^{-5+5} + 6 = -4^{0} + 6 = -1 + 6 = 5$$ Point: $$(-5, 5)$$ - For $$x = -4$$: $$f(-4) = -4^{-4+5} + 6 = -4^{1} + 6 = -4 + 6 = 2$$ Point: $$(-4, 2)$$ 4. **Summary:** - The asymptote is horizontal at $$y = 6$$. - Two points to plot are $$(-5, 5)$$ and $$(-4, 2)$$. These points show the exponential decay reflected across the x-axis, shifted left by 5 units and up by 6 units.