List the intercepts and type(s) of symmetry, if any.
-$$y = \frac { - x ^ { 5 } } { x ^ { 2 } - 6 }$$
A) intercept: $( 0,0 )$
symmetric with respect to origin

B) intercept: $( 0,0 )$
symmetric with respect to $x$-axis

C) intercepts: $( \sqrt { 6 } , 0 ) , ( - \sqrt { 6 } , 0 ) , ( 0,0 )$
symmetric with respect to origin

D) intercept: $( 0,0 )$
symmetric with respect to $\mathrm { y }$-axis

Question

List the intercepts and type(s) of symmetry, if any.
-$$y = \frac { - x ^ { 5 } } { x ^ { 2 } - 6 }$$
A) intercept: $( 0,0 )$
symmetric with respect to origin

B) intercept: $( 0,0 )$
symmetric with respect to $x$-axis

C) intercepts: $( \sqrt { 6 } , 0 ) , ( - \sqrt { 6 } , 0 ) , ( 0,0 )$
symmetric with respect to origin

D) intercept: $( 0,0 )$
symmetric with respect to $\mathrm { y }$-axis

Quizplus · Accepted Answer

The given function is odd, as replacing $x$ with $-x$ results in the original function being multiplied by $-1$, indicating symmetry with respect to the origin. There are no $x$-intercepts because the numerator and denominator share no common factors that would allow for $x$ to be set to zero in the equation. The $y$-intercept occurs when $x=0$, which also results in $y=0$, hence the intercept is $(0,0)$.

List the Intercepts and Type(s) of Symmetry, If Any y=−x5x2−6y = \frac { - x ^ { 5 } } { x ^ { 2 } - 6 }y=x2−6−x5​

List the Intercepts and Type(s) of Symmetry, If Any $y = \frac { - x ^ { 5 } } { x ^ { 2 } - 6 }$