Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing the function with a graphing utility, if one is available. $y = \frac { 8 x - 7 } { x ^ { 2 } + 36 }$
A)discontinuous at $x = - 36$
B)discontinuous at $x = 6$
C)discontinuous at $x = - 6$
D)discontinuous at $x = 36$
E)continuous everywhere

Question

Quizplus · Accepted Answer

The function $y = \frac { 8 x - 7 } { x ^ { 2 } + 36 }$ is continuous everywhere because the denominator $x^2 + 36$ is never zero for any real value of $x$. The expression $x^2 + 36$ is always positive, so there are no points of discontinuity.

Determine Whether the Given Function Is Continuous y=8x−7x2+36y = \frac { 8 x - 7 } { x ^ { 2 } + 36 }y=x2+368x−7​

Determine Whether the Given Function Is Continuous $y = \frac { 8 x - 7 } { x ^ { 2 } + 36 }$