1. The problem is to graph the function $$y=\frac{1}{3}x + 1$$ and find its domain and range. 2. The formula given is a linear function in slope-intercept form $$y=mx+b$$ where $$m=\frac{1}{3}$$ is the slope and $$b=1$$ is the y-intercept. 3. The domain of a linear function is all real numbers because you can input any value of $$x$$ and get a corresponding $$y$$. 4. The range of a linear function is also all real numbers because as $$x$$ goes to positive or negative infinity, $$y$$ will also go to positive or negative infinity. 5. To graph, start at the y-intercept (0,1). 6. Use the slope $$\frac{1}{3}$$ which means rise 1 unit up and run 3 units right to find another point (3,2). 7. Draw a straight line through these points extending in both directions. 8. Final answers: - Domain: $$(-\infty, \infty)$$ - Range: $$(-\infty, \infty)$$