Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative.
-$$f ( x ) = \frac { x - 2 } { ( x - 4 ) \sqrt { x + 6 } }$$
A) (a) $\{ 2 \}$, (b) $\{ 4 \} \cup ( \infty , - 6 )$, (c) $( - 6,2 ) \cup ( 4 , \infty )$, (d) $( 2,4 )$
B) (a) $\{ 2,4 \}$, (b) $( - \infty , - 6 )$, (c) $( - 6,2 ) \cup ( 4 , \infty )$, (d) $( 2,4 )$
C) (a) $\{ 2 \}$, (b) $\{ 4 \} \cup (\infty, - 6 )$, (c) $( 2,4 )$, (d) $( - 6,2 ) \cup ( 4 , \infty )$
D) (a) $\{ 2,4 \}$, (b) $( \infty , - 6 )$, (c) $( 2,4 )$, (d) $( - 6,2 ) \cup ( 4 , \infty )$

Question

Quizplus · Accepted Answer

- For (a), the function is zero when the numerator is zero, which happens at $x = 2$.- For (b), the function is undefined when the denominator is zero or the square root is undefined. This occurs at $x = 4$ and for $x < -6$.- For (c), the function is positive when the numerator and denominator have the same sign. This happens for $x > 4$ and for $-6 < x < 2$, since the square root is always positive.- For (d), the function is negative between the zero of the numerator and the zero of the denominator, which is for $2 < x < 4$.

Determine the X Values That Cause the Function to Be f(x)=x−2(x−4)x+6f ( x ) = \frac { x - 2 } { ( x - 4 ) \sqrt { x + 6 } }f(x)=(x−4)x+6​x−2​

Determine the X Values That Cause the Function to Be $f ( x ) = \frac { x - 2 } { ( x - 4 ) \sqrt { x + 6 } }$