1. The problem asks us to graph the logarithmic function $$g(x) = -\log_4 x + 1$$ and plot two points as well as the vertical asymptote. 2. The logarithmic function $$\log_4 x$$ has domain $$x > 0$$ and a vertical asymptote at $$x=0$$ because logarithm is undefined for non-positive values. 3. The function $$g(x) = -\log_4 x + 1$$ flips the graph of $$\log_4 x$$ vertically (due to the negative sign) and shifts it up by 1 unit. 4. To plot two points, choose convenient $$x$$ values in the domain $$x>0$$. 5. Let $$x=1$$, then: $$g(1) = -\log_4 1 + 1 = -0 + 1 = 1$$ Point: $$(1, 1)$$ 6. Let $$x=4$$, then: $$g(4) = -\log_4 4 + 1 = -1 + 1 = 0$$ Point: $$(4, 0)$$ 7. The vertical asymptote is the line $$x=0$$. 8. The domain of $$g$$ is $$x > 0$$ (all positive real numbers). 9. The range of $$g$$ is all real numbers $$(-\infty, +\infty)$$ because the logarithm function extends infinitely as $$x$$ approaches 0 from the right and as $$x$$ becomes very large. Final answers: - Two points: $$(1,1)$$ and $$(4,0)$$ - Vertical asymptote: $$x=0$$ - Domain: $$x > 0$$ - Range: $$(-\infty, +\infty)$$