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Determine if the given function has any points of discontinuity. Explain your reasoning.

f(x) = (x^2-b^2)/(x-b)

A. There is a point of discontinuity at x = b because the denominator has the factor x – b.
B. There are points of discontinuity at both x = – b and x = b because the numerator has factors of x + b and x – b.
C. There is a point of discontinuity at x = b only because the factor of x – b is common to both the numerator and denominator.
D. There is a point of discontinuity at x = –b only because the factor of x – b is common to both the numerator and denominator and factors out.

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Answer:

C) There is a point of discontinuity at x = b only because the factor of x – b is common to both the numerator and denominator.

Step-by-step explanation:

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The given function represents that there should be the point of discontinuity at x = b only because the factor of x – b is common to both the numerator and denominator.

Given that,

  • The function is [tex]f(x) = (x^2-b^2)\div (x-b)[/tex].

Based on the above information, the information is as follows:

  • As we can see that there should be the point of discontinuity at x = b only as the factor of x - b should be common for both numerator and denominator.

Learn more: brainly.com/question/17429689

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