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A.4.1.2 Be Right Back!

Three days in a row, a dog owner tied his dog’s 5-foot-long leash to a post outside a store while he ran into the store to get a drink. Each time, the owner returned within minutes. These things are true every day: Each day, the dog was 1.5 feet away from the post when the owner left. Each day, 60 seconds after the owner left, the dog was 4 feet from the post. Below is an additional description of the dog's other unique daily behavior for 3 different days. Use the pen tool to sketch a graph that could represent the dog’s distance from the post, in feet, as a function of time, in seconds, since the owner left.
Day 1: The dog walked around the entire time while waiting for its owner.
Day 2: The dog walked around for the first minute, and then laid down until its owner returned.
Day 3: The dog tried to follow its owner into the store but was stopped by the leash. Then, it started walking around the post in one direction. It kept walking until its leash was completely wound up around the post. The dog stayed there until its owner returned.

Is the relationship between the time the owner left and the dog's distance from the a function? Explain how you know.

In this situation (about time and dog's distance from post), what is the independent variable (input or x) and what is the dependent variable (output or y)?