# How to tell if a function is continuous without graphing

Learning How to tell if a function is continuous without graphing is an essential part of life - so let’s get solving together.

## Continuous Functions

Your pre-calculus teacher will tell you that three things have to be true for a function to be continuous at some value c in its domain: f(c) must be defined. The function must exist ## How to Determine Whether a Function Is Continuous or

In some case, there is no easy way to tell without just directly checking the definition. The piecewise function f (0)=1, f (x)=sin (x)/x for x nonzero is continuous, but it's not obvious that it Deal with mathematic

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## 2.6: Continuity

Solution : By observing the given graph, we come to know that. lim x-> x0- f (x) = f (x 0 ) (Because we have filled circle) But, lim x-> x0+ f (x) ≠ f (x 0 ) (Because we have unfilled circle) Hence ## Calculus I

In plain English, a real function f is continuous if you can draw its graph without lifting your pen. Id est, if the set of points {(x,f(x))} is a path-connected set. (This is a little circular since you need

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## How does one determine whether a function is continuous or

From the above definitions, we can define three conditions to check the continuity of the given function. They are: Consider the function f (x) and point x = a. 1. The function must be defined 