# How To Know If A Function Is Continuous Or Discontinuous

A function is continuous if given any two points within the function’s domain, there exists a smooth curve that connects those points. A function is discontinuous if there is a point within the domain at which the function produces two different results.
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In order to determine if a function is continuous or discontinuous, one must first examine the function’s domain. If the function produces the same result regardless of how two points within the domain are connected, then the function is continuous. If the function produces two different results depending on how those points are connected, then the function is discontinuous.

### How Do You Tell If A Function Is Discontinuous On A Graph?

A function is discontinuous if there is a point on the graph where the function is not defined or the function changes abruptly.

There are three types of discontinuities:

1) A point discontinuity is a discontinuity at a specific point on the graph. For example, if a function is defined as f(x) = x^2 – 4 and there is a point on the graph where x = 2, then the function is discontinuous at that point.

2) A jump discontinuity is a discontinuity where the function changes abruptly. For example, if a function is defined as f(x) = x^2 – 4 and there is a point on the graph where x = 2, then the function is discontinuous at that point.

3) An essential discontinuity is a discontin

### What Makes A Function Discontinuous?

A function is discontinuous if it is not continuous. There are many ways for a function to be discontinuous.

One way a function can be discontinuous is if it has a hole in it.
This means that there is a point in the domain of the function where the function is undefined.

Another way a function can be discontinuous is if it is not differentiable at a point in its domain.
This means that the function has a sudden change in slope at that point.

A function can also be discontinuous if it has a infinite discontinuity.
This means that the function has a point in its domain where the function values approach infinity or negative infinity.

### What Are Continuous And Discontinuous Functions With Examples?

A continuous function is a function that can be drawn without lifting the pen, meaning that given any two points within the function’s domain, there exists a smooth curve that connects those points. An example of a continuous function is y=x^2. A discontinuous function is a function that cannot be drawn without lifting the pen, meaning that there exists at least two points within the function’s domain such that there does not exist a smooth curve that connects those points. An example of a discontinuous function

### What Are The 3 Conditions Of Continuity?

The three conditions of continuity are as follows: (1) The function f(x) must be defined for all values of x in the interval [a, b].
(2) The function f(x) must be continuous at each point x in the interval [a, b].
(3) The function f(x) must have a continuous derivative for all values of x in the interval [a, b].

### What Makes A Function Continuous?

A function is continuous if given any two points within the function’s domain, there exists a smooth curve that connects those points. A function is discontinuous if there is a point within the domain at which the function produces two different outputs.

### What Are Examples Of Discontinuous Functions?

A discontinuous function is a function that is not continuous.

Some examples of discontinuous functions are the following:

-The function f(x) = 1/x is discontinuous at x = 0.

-The function f(x) = |x| is discontinuous at x = 0.

-The function f(x) = sqrt(x) is discontinuous at x = 0.

### How Do You Find The Discontinuity?

There is a discontinuity at x=-2. To find it, you would set the function equal to 0 and solve for x.

### What Makes A Function Continuous?

A function is continuous if given any two points within the function’s domain, there exists a smooth curve that connects those points. A function is also continuous if given a point within the domain and a small enough neighborhood around that point, the function’s image is completely contained within that neighborhood.

### How Do You Find The Continuity Of A Function?

There are many ways to find the continuity of a function. One way is to use the definition of continuity. A function is continuous if given any small enough number, ε, there exists a corresponding small enough number, δ, such that whenever x is within δ units of a, f(x) is within ε units of f(a).

### What Can You Say About The Continuous Function?

A continuous function is a function that does not have any gaps or breaks in its graph. A function is continuous if given any two points within the function’s domain, there exists a smooth curve (not necessarily a straight line) that connects those points.

### Which Functions Are Not Continuous?

There are many functions which are not continuous. Some examples are the function which is equal to 1 for all x except at 0, where it is equal to 0. Another example is the function which is equal to 1/x.