Determine the interval (s) where the following function is continuousx-7f(x)= (x-7)x+4)

Answered: Determine the interval (s) where the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Determine the interval (s) where the following function is continuous
x-7
f(x)= (x-7)x+4)

Expert Solution

Step 1

In the given function (x-7) is a common factor in numerator and denominator. So, it will cancel out and it gives the more simplified function.

Step 2

A rational function is continuous for all real numbers except at points where its denominator is 0.
So, in order to find the interval of continuity for the function we have to find a interval of x for which the denominator, x(x+4) is not equal to 0.
It can be clearly seen that x(x+4) is equal to 0 at x = 0 and at x = -4.
Therefore, the given function is continuous for all x belongs to real number except at x =0, -4.