Final answer:
The statement that an absolute value function has a graph that is totally smooth is true; the graph is a continuous V-shaped curve that is piecewise linear.
Step-by-step explanation:
An absolute value function has a graph that is totally smooth. This statement is true. Absolute value functions are represented graphically as a V-shaped curve that opens upwards, and this curve is a piecewise linear function that is continuous and has no breaks, jumps, or pointed corners at the vertex. Therefore, the graph of an absolute value function is smooth. It's important to note that while the graph is smooth, the vertex of the V-shape has a distinct corner, which represents a change in direction but not a lack of smoothness.