Final answer:
The graph of g(x) = |x - 5| is a V-shaped graph with its vertex at (5, 0), the domain is all real numbers, and the range is all non-negative real numbers.
Step-by-step explanation:
The graph of the function g(x) = |x - 5| is a V-shaped graph. This is because the absolute value function takes all negative inputs and makes them positive, which causes the graph to reflect across the x-axis when x is less than 5. The vertex of this graph appears when the expression inside the absolute value is zero; hence for g(x), the vertex is at (5, 0).
The domain of g(x) is all real numbers because there are no restrictions on the values that x can take, so the domain is (-∞, +∞). The range is all non-negative real numbers since the absolute value is always zero or positive, and so the range is [0, +∞). When sketching the graph, it is crucial to scale the x and y axes and label the graph with g(x) and x correctly.