Answer the question about the given function.
-Given the function $f ( x ) = \frac { x ^ { 2 } + 5 } { x - 3 }$, list the $x$-intercepts, if any, of the graph of $f$.
A) $( 3,0 )$
B) $( 5,0 ) , ( - 5,0 )$
C) $( - \sqrt { 5 } , 0 )$
D) none

Question

Quizplus · Accepted Answer

The $x$-intercepts of a function occur where $f(x) = 0$. For the given function $f(x) = \frac{x^2 + 5}{x - 3}$, setting the numerator equal to zero gives $x^2 + 5 = 0$, which has no real solutions since $x^2 = -5$ is not possible for real numbers. Therefore, the function has no $x$-intercepts.

Answer the Question About the Given Function f(x)=x2+5x−3f ( x ) = \frac { x ^ { 2 } + 5 } { x - 3 }f(x)=x−3x2+5​

Answer the Question About the Given Function $f ( x ) = \frac { x ^ { 2 } + 5 } { x - 3 }$