1. The problem asks which of the points A-F lies on the curve defined by the equation $$y=\frac{1}{x-3}$$. 2. To check if a point $(x,y)$ lies on the curve, substitute the $x$-coordinate into the equation and see if the resulting $y$ matches the point's $y$-coordinate. 3. Let's check each point: - Point A: $(1,1)$ $$y=\frac{1}{1-3}=\frac{1}{-2}=-0.5$$ The point's $y$ is 1, which does not equal $-0.5$. - Point B: $(1,0.5)$ $$y=\frac{1}{1-3}=\frac{1}{-2}=-0.5$$ The point's $y$ is 0.5, which does not equal $-0.5$. - Point C: $(1,0)$ $$y=\frac{1}{1-3}=\frac{1}{-2}=-0.5$$ The point's $y$ is 0, which does not equal $-0.5$. - Point D: $(0,1)$ $$y=\frac{1}{0-3}=\frac{1}{-3}=-0.333...$$ The point's $y$ is 1, which does not equal $-0.333...$. - Point E: $(0,0.5)$ $$y=\frac{1}{0-3}=\frac{1}{-3}=-0.333...$$ The point's $y$ is 0.5, which does not equal $-0.333...$. - Point F: $(0,0)$ $$y=\frac{1}{0-3}=\frac{1}{-3}=-0.333...$$ The point's $y$ is 0, which does not equal $-0.333...$. 4. None of the points A-F satisfy the equation $y=\frac{1}{x-3}$ exactly. Final answer: None of the points A-F lie on the curve $y=\frac{1}{x-3}$.