Final answer:
The questions are about the properties and behavior of functions in mathematics, including continuity and slopes of functions, and probability density functions for continuous random variables.
Step-by-step explanation:
The subject of the questions presented revolves around the concept of functions and their properties. Functions are fundamental components in mathematics, often defined by an equation that describes a relationship between two sets of numbers where each input has a single output.
For a function f(x) to be continuous, it means there are no breaks, jumps, or holes in its graph and it can be drawn without lifting the pencil off the paper. If f(x) is said to have a positive slope, this indicates that as x increases, the value of f(x) also increases.
A probability function, also known as a probability density function in the context of continuous random variables, assigns probabilities to intervals in its domain. For continuous probability distributions, properties such as P(x > a), where 'a' is a number in the domain of the function, refer to the probability of the continuous random variable being greater than 'a', which can be found using the area under the probability density function curve.