Question 253049
The answer is D.

For {{{ x=0 }}} , the function evaluates to 2. Furthermore, since the function is strictly decreasing as {{{ x }}} increases (its derivative is negative for all {{{ x > 0 }}} ), all positive values evaluate to strictly less than 2. Lastly, the fraction has a vertical asymptote of {{{ y = 1 }}} (the ratio of the leading coefficients of numerator and denominator), which means the expression is also strictly larger than 1.
In conclusion, for all positive integers, the function always evaluates to strictly less than 2 and strictly larger than 1, hence, never an integer.

{{{ graph( 600, 300, -10, 100, -1, 3, (x+4)/(x+2)) }}}

Answer B is not correct, as for {{{ x = 1 }}} it evaluates to 0, which is an integer.