Question

question 14 (5 points)
listen
state whether the graph of $-\frac{4}{x^{2}}$ has infinite discontinuity, jump discontinuity, point discontinuity, or is continuous.
the function is continuous.
the function has infinite discontinuity.
the function has point discontinuity.
the function has jump discontinuity.

Explanation:

Step1: Analyze the domain of the function

The function \(y =-\frac{4}{x^{2}}\) is not defined when \(x = 0\) since division by zero is undefined.

Step2: Analyze the limit as \(x\) approaches \(0\)

We calculate the limit \(\lim_{x
ightarrow0}-\frac{4}{x^{2}}\). As \(x\) approaches \(0\) (either from the left \(x
ightarrow0^{-}\) or from the right \(x
ightarrow0^{+}\)), \(x^{2}
ightarrow0^{+}\). Then \(\lim_{x
ightarrow0}-\frac{4}{x^{2}}=-\infty\)

Answer:

The function has infinite discontinuity.