Final answer:
An absolute value function fails the horizontal line test because its 'V' shape intersects a horizontal line at two points, indicating that it is not one-to-one.
Step-by-step explanation:
An absolute value function, which is represented as f(x) = |x|, has a characteristic 'V' shape. This shape means that for every positive value of 'x', there is a corresponding negative value of 'x' that yields the same result after taking the absolute value. Because of this reflection across the y-axis, the graph of an absolute value function will fail the horizontal line test. The horizontal line test is used to determine if a function is one-to-one and whether or not it has an inverse that is also a function. Since a horizontal line drawn across the 'V' shape of the absolute value function would intersect it in two places, it fails the test, indicating the function is not one-to-one.
A function would pass the vertical line test if, for each x-value, there is only one y-value. This is true for absolute value functions, so they indeed pass the vertical line test, confirming they are indeed functions. The other options mentioned, such as the regression formula test and the exponential formula test, are not standard methods to assess the attributes of basic functions like absolute value.
Statements regarding other types of graphs, such as a horizontal line at a positive or negative value, refer to different contexts, such as velocity or acceleration graphs in physics, not to characteristics of absolute value functions in mathematics.