What defines an increasing function in terms of output values?

An increasing function is characterized by the relationship between its input and output values, specifically that as the input values increase, the output values also increase. This means if you take any two inputs (x_1) and (x_2) such that (x_1 < x_2), the output value (f(x_1)) will be less than or equal to (f(x_2)). In simple terms, for a function to be classified as increasing, it should produce higher output values as the corresponding input values are raised, which directly aligns with the definition provided in the correct choice.

Understanding this is crucial for analyzing functions in mathematics, as it allows for making predictions about the behavior of the function over its domain, and is foundational in calculus and algebra when studying function trends.