# When Can You Say That A Function Is Continuous Or Discontinuous?

## When can we say that a function is continuous?

Saying a function f is continuous when x=c is the same as saying that the function’s two-side limit at x=c exists and is equal to f(c)..

## What are the 3 types of discontinuity?

Continuity and Discontinuity of Functions Functions that can be drawn without lifting up your pencil are called continuous functions. You will define continuous in a more mathematically rigorous way after you study limits. There are three types of discontinuities: Removable, Jump and Infinite.

## Where is a function discontinuous on a graph?

We say the function is discontinuous when x = 0 and x = 1. There are 3 asymptotes (lines the curve gets closer to, but doesn’t touch) for this function. They are the x-axis, the y-axis and the vertical line x=1 (denoted by a dashed line in the graph above).

## Is a function discontinuous at a hole?

The function is not continuous at this point. This kind of discontinuity is called a removable discontinuity. Removable discontinuities are those where there is a hole in the graph as there is in this case. … In other words, a function is continuous if its graph has no holes or breaks in it.

## How do you know if a function is continuous or discontinuous?

A function being continuous at a point means that the two-sided limit at that point exists and is equal to the function’s value. Point/removable discontinuity is when the two-sided limit exists, but isn’t equal to the function’s value.

## Is a square root function continuous or discontinuous?

√x is continuous everywhere it exists. By definition if the approaches differ, or if one doesn’t exist, the limit is undefined, so the function can’t be continuous.

## Do discontinuous functions have limits?

A finite discontinuity exists when the two-sided limit does not exist, but the two one-sided limits are both finite, yet not equal to each other. The graph of a function having this feature will show a vertical gap between the two branches of the function. The function f(x)=|x|x has this feature.

## Can a function be continuous and not differentiable?

In particular, any differentiable function must be continuous at every point in its domain. The converse does not hold: a continuous function need not be differentiable. For example, a function with a bend, cusp, or vertical tangent may be continuous, but fails to be differentiable at the location of the anomaly.

## What are the 3 conditions of continuity?

Note that in order for a function to be continuous at a point, three things must be true: The limit must exist at that point. The function must be defined at that point, and. The limit and the function must have equal values at that point.

## What is the difference between continuous and discontinuous piecewise functions?

The piecewise function shown in this example is continuous (there are no “gaps” or “breaks” in the plotting). … Piecewise defined functions may be continuous (as seen in the example above), or they may be discontinuous (having breaks, jumps, or holes as seen in the examples below).

## How do you find where a function is discontinuous?

Start by factoring the numerator and denominator of the function. A point of discontinuity occurs when a number is both a zero of the numerator and denominator. Since is a zero for both the numerator and denominator, there is a point of discontinuity there. To find the value, plug in into the final simplified equation.

## Can functions be discontinuous?

Discontinuous functions are functions that are not a continuous curve – there is a hole or jump in the graph. It is an area where the graph cannot continue without being transported somewhere else.