How do you prove a function is continuous at all points?

If f(x) = F(G(x)), then f is continuous at all points in its domain if G is continuous at all points in its domain and F is continuous at all points in its domain. ( Note that we can repeat the process to get the same result for a function of the form F(G(H(x))). )

How do you tell if a function is continuous or discrete?

A discrete function is a function with distinct and separate values. A continuous function, on the other hand, is a function that can take on any number within a certain interval. Discrete functions have scatter plots as graphs and continuous functions have lines or curves as graphs.

What is a continuous function?

In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there is no abrupt changes in value, known as discontinuities.

What is a real life example of a continuous function?

Suppose you want to use a digital recording device to record yourself singing in the shower. The song comes out as a continuous function.

How do you know if something is discrete or continuous?

Definition: A set of data is said to be continuous if the values belonging to the set can take on ANY value within a finite or infinite interval. Definition: A set of data is said to be discrete if the values belonging to the set are distinct and separate (unconnected values).

What are examples of continuous data?

Height, weight, temperature and length are all examples of continuous data. Some continuous data will change over time; the weight of a baby in its first year or the temperature in a room throughout the day.

How do you make data continuous?

Answer Expert Verified In order to make class intervals continuous, you are supposed to subtract 0.5 from the lower limit and add 0.5 in the upper limit.