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 continuous if given any two points within the function’s domain, there exists a smooth curve that connects those points.

### How Do You Know If A Graph Is Continuous Or Discontinuous?

A graph is continuous if it is a smooth curve. A graph is discontinuous if it has any gaps or breaks in it.

A graph is continuous if it is a smooth curve. A graph is discontinuous if it has any gaps or breaks in it.

### What Is A Continuous Function On A Graph?

A continuous function on a graph is a function that is defined for all points on the graph.

A function is continuous if given any two points within the function’s domain, there exists a smooth curve that connects those points.

### Can You Tell If A Function Is Continuous?

There is no definitive answer to this question, as continuity is a relative concept. In general, however, one can often tell if a function is continuous by looking at its graph. If the graph is a smooth curve with no sharp corners or discontinuities, then the function is likely to be continuous.

### What Are The 3 Conditions Of Continuity?

The three conditions of continuity are as follows: (1) The function must be defined for all values of x in the given interval.

(2) The function’s graph must be a single, unbroken curve.

(3) The function’s graph must have no gaps or holes.

### How Do You Know If A Function Is Continuous Everywhere?

There is no definitive answer to this question, as there is no single definition of “continuity.” Some definitions of continuity require a function to be continuous everywhere, while others allow for functions to be discontinuous at certain points. In general, however, one can usually tell if a function is continuous by looking at its graph. If the graph is smooth and uninterrupted, then the function is likely continuous. If the graph has any sharp points or discontinuities, then the function is likely discontinuous.

### 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 value, ε, there exists a point within the domain such that the function’s value is within ε units of the given point.

### What Defines A Continuous Function?

A continuous function is a function that does not have any abrupt changes in its output. A function is continuous if given any two points within its domain, there exists a smooth curve that connects those points.”

A function is continuous if given any two points within its domain, there exists a smooth curve that connects those points.

### What Makes A Graph Discontinuous?

A graph is discontinuous if it has any gaps in it. A graph is also discontinuous if it is not a function.

### What Makes A Graph Discontinuous?

A graph is discontinuous if it has any gaps in it. A function is discontinuous if its graph has any gaps in it.

### How Do You Find Where A Function Is Discontinuous?

A function is discontinuous if it is not continuous. There are three types of discontinuities:

1. Point discontinuity:

A function has a point discontinuity at x=a if it is not defined at that point, but is defined on either side of that point.

2. Jump discontinuity:

A function has a jump discontinuity at x=a if it is defined at that point, but the left-hand limit and the right-hand limit of the function at that point are not equal.

3. Infinite discontinuity:

A function has an infinite discontinuity at x=a if it is not defined at that point, and the left-hand limit or the right-hand limit of the function at that point

### 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.

### What Functions Are Not Continuous?

There are many functions that are not continuous. Some examples include the function f(x) = 1/x, which is not continuous at x = 0, and the function f(x) = |x|, which is not continuous at x = 0.

### Which Of The Following Is True For Continuous Functions?

All of the above.

A continuous function is a function that is defined for all values in its domain. A continuous function is a function that is continuous at every point in its domain. A continuous function is a function that has a continuous derivative at every point in its domain.

### 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).