Use a graph to determine whether the given function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity. $g ( x ) = \frac { 3 } { x ^ { 2 } - 16 }$
A)The function is continuous on its domain.
B) The points of discontinuity: 16, 0.
C) The points of discontinuity: $\frac { 1 } { 3 }$ , 0.
D) The point of discontinuity: 0.
E) The point of discontinuity: 16.

Question

Use a graph to determine whether the given function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity.   $g ( x ) = \frac { 3 } { x ^ { 2 } - 16 }$  
A)The function is continuous on its domain.
B) The points of discontinuity: 16, 0.
C) The points of discontinuity: $\frac { 1 } { 3 }$ , 0.
D) The point of discontinuity: 0.
E) The point of discontinuity: 16.

Quizplus · Accepted Answer

The function $g(x) = \frac{3}{x^2 - 16}$ is continuous everywhere except where the denominator equals zero. The denominator $x^2 - 16 = 0$ when $x = \pm 4$, but these points are not listed in any of the options, indicating a misunderstanding in the question's formulation. However, based on the provided options, the correct interpretation is that the function is considered continuous on its domain, which excludes the points where the denominator is zero, thus not directly listing points of discontinuity in the options.

Use a Graph to Determine Whether the Given Function Is g(x)=3x2−16g ( x ) = \frac { 3 } { x ^ { 2 } - 16 }g(x)=x2−163​

Use a Graph to Determine Whether the Given Function Is $g ( x ) = \frac { 3 } { x ^ { 2 } - 16 }$