Final answer:
The function f(x) = |x| + 1 is graphed as two lines forming a V-shaped graph with the lowest point at (0,1). The domain is all real numbers, and the range is [1, ∞). The graph demonstrates a characteristic 45-degree rise for both positive and negative x-values.
Step-by-step explanation:
The function you are working with is f(x) = |x| + 1. To graph this function, you would plot two different pieces. When x is positive, the graph is simply the line y = x + 1, which starts at (0, 1) and goes upwards at a 45-degree angle. When x is negative, the graph is y = -x + 1, which is also a 45-degree line but rising as you move leftward from the y-axis.
The domain of f(x) is all real numbers, since there are no restrictions on the values x can take. As for the range, since the absolute value function ensures all outputs are non-negative, and we add 1, the range starts from 1 and goes to infinity. Therefore, the domain is (-∞, ∞), and the range is [1, ∞).
To accurately construct the graph, label the x-axis with numbers from -20 to 20 (or a smaller range if detailing a specific part of the graph). Label the y-axis similarly, noting that the function will never go below y = 1. The graph will have a V-shape with the point of the V at (0,1), demonstrating that no matter the x-value, the output of the function will always be greater than or equal to 1.