Modeling with Rational and Piecewise-Defined Functions: Part Two — Test

Question 11 • Precalculus

Which function is continuous at x is equal to 18 ?

Answer

f of x is equal to the fraction with numerator open paren x minus 18 close paren squared and denominator x

f of x is equal to tangent of open paren pi over 36 x close paren

f of x is equal to the fraction with numerator x squared minus 17 x minus 18 and denominator x minus 18

f of x inequality x squared comma x is not equal to 18 inequality 36 comma comma x equals 18

Explanation

A function is continuous at x = 18 if it is defined there and its limit equals its value. In choice A, the denominator is x, which is 18 at x = 18, so it is not zero; the function is defined and continuous there. Choice B is undefined because tan(π/2) does not exist, and choice C has a zero denominator at x = 18. In choice D, the function’s value is 36, but nearby values approach 18² = 324.

AI-written and checked against the verified answer.

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