# Is the function h(x) = 3x + 2 for x less than 4 and 18-x for x greater than 4 continuous at the...

## Question:

Is the function {eq}h(x)=\left\{\begin{matrix} 3x+2 & \mathrm{for}\;x<4\\ 18-x & \mathrm{for}\; x > 4 \end{matrix}\right. {/eq} continuous at the point {eq}x = 4 {/eq}?

## Continuous function:

A trivial definition of a continuous function is that If the graph that defines the function can be traced without lifting the finger from the paper, that is, if the function can be traced with a single stroke, then it is continuous.

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Given the function

\begin{align} h(x)=\left\{\begin{matrix} 3x+2 & \mathrm{for}\; x<4\\ 18-x & \mathrm{for}\; x >...

How to Determine if a Limit Does Not Exist

from

Chapter 4 / Lesson 9
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Determining if a limit does not exist requires information about the limit type, its asymptote, and graphed point. Study the formulas associated with finding these metrics and how they are used to determine whether right-hand, left-hand, or two-sided limits exist for a function.