Which of the following is a rational function?

A) $f ( x ) = \frac { \lfloor x \rfloor + 3 } { x - 2 }$
B) $f ( x ) = \frac { | x | ^ { 2 } + 5 } { x + 1 }$
C) $f ( x ) = \frac { \sqrt { x } - 5 } { \sqrt { x - 5 } }$
D) $f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + \frac { 5 } { \sqrt { x } }$
E) $f ( x ) = \frac { 3 } { 2 } x ^ { 2 } - \frac { 11 } { x }$

Question

Which of the following is a rational function?

A) $f ( x ) = \frac { \lfloor x \rfloor + 3 } { x - 2 }$
B) $f ( x ) = \frac { | x | ^ { 2 } + 5 } { x + 1 }$
C) $f ( x ) = \frac { \sqrt { x } - 5 } { \sqrt { x - 5 } }$
D) $f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + \frac { 5 } { \sqrt { x } }$
E) $f ( x ) = \frac { 3 } { 2 } x ^ { 2 } - \frac { 11 } { x }$

Quizplus · Accepted Answer

A rational function is defined as a function that can be expressed as the quotient of two polynomials. Choice E, $f(x) = \frac{3}{2}x^2 - \frac{11}{x}$, can be rewritten as $f(x) = \frac{3}{2}x^2 - \frac{11}{x} = \frac{3x^3 - 22}{2x}$, which is a quotient of two polynomials, making it a rational function. Choices A, B, C, and D involve operations (floor function, absolute value, square root) that do not allow them to be expressed solely as the quotient of two polynomials.

Which of the Following Is a Rational Function? A) f(x)=⌊x⌋+3x−2f ( x ) = \frac { \lfloor x \rfloor + 3 } { x - 2 }f(x)=x−2⌊x⌋+3​

Which of the Following Is a Rational Function?

A) $f ( x ) = \frac { \lfloor x \rfloor + 3 } { x - 2 }$