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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 14: Q. 14 (page 905)

In Problem, determine whether f is continuous at c.
$f (x) = \{\begin{cases} \frac{x^{2} - 4}{x + 2}, x 鈮� - 2 \\ 4, x = - 2 \end{cases}, c = - 2$

Short Answer

Expert verified

The given polynomial function $f (x) = \{\begin{cases} \frac{x^{2} - 4}{x + 2}, x 鈮� - 2 \\ 4, x = - 2 \end{cases}, c = - 2$
is not continuous

Step by step solution

01

Step.1 Given information

Polynomial function $f (x) = \{\begin{cases} \frac{x^{2} - 4}{x + 2}, x 鈮� - 2 \\ 4, x = - 2 \end{cases}, c = - 2$

c=-2

We know that

A function is called continuous function when at x= a,

$\underset{x 鈫� a}{l i m} f (x) = f (a)$

and defined for every number of domain

and $\underset{x 鈫� c}{f (x}) = A a n d f (c) = A$

02

Step2. Calculations of checking of continuity

Assume that x=-2 is in the domain of the given function, so we can proceed to find the continuity, for continuity x is the approach to -2,

so according to question

$f (x) = \frac{x^{2} - 4}{x + 2} f (x) = \frac{(x + 2) (x - 2)}{(x + 2)} f (x) = x - 2 \underset{x 鈫� - 2}{f (x)} = - 2 - 2 = - 4$

but in question f(-2)= 4

so, $\underset{x 鈫� c}{f (x) 鈮�} f (c)$ , the function is not continuous

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