26:I[49711,["/_next/static/chunks/0t1_7x_uuxe34.js","/_next/static/chunks/0~ta-e_o9dqvm.js","/_next/static/chunks/115lbazto1qq7.js","/_next/static/chunks/0vq81gpimz.3f.js","/_next/static/chunks/0jal2z51-yxb_.js"],"default"] 27:T4d4,A jump discontinuity (or step discontinuity) occurs at $x$-values where the one-sided limits exist but aren't equal. [[graph 1]] Looking at the graph we can see that $\lim\limits_{x \to 0^-} g(x) = -4$ while $\lim\limits_{x \to 0^+} g(x) = 0$. Therefore, $g$ has a jump discontinuity at $x=0$. Similarly, we can see that $\lim\limits_{x \to 6^-} g(x) \approx 7.5$ while $\lim\limits_{x \to 6^+} g(x) = 3$. Therefore, $g$ has a jump discontinuity at $x=6$. $g$ is continuous at $x=2$. So this answer is incorrect. **In conclusion, $x=0$ and $x=6$ are the only values where $g$ has jump discontinuities.** --- Licensing information: The question comes from Khan Academy, and is licensed under a creative commons license. The original test containing this question can be found here: Unit Test. Note: All Khan Academy content is available for free at www.khanacademy.org. 28:T4d3,A removable discontinuity occurs at points where the two-sided limit exists but doesn't equal the function value at that point. [[graph 1]] Looking at the graph we can see that $\lim\limits_{x \to -3}f(x) = -5$ while $f(-3)$ is undefined. Therefore, $f$ has a removable discontinuity at $x = -3$. Similarly, we can see that $\lim\limits_{x \to 6} f(x) =2$ while $f(6)=4$. Therefore, $f$ has a removable discontinuity at $x=6$. $f$ has a vertical asymptote at $x = -1$. So this answer is incorrect. **In conclusion, $x = -3$ and $x = 6$ are the only values where $f$ has removable discontinuities.** --- Licensing information: The question comes from Khan Academy, and is licensed under a creative commons license. The original exercise containing this question can be found here: Classify discontinuities. Note: All Khan Academy content is available for free at www.khanacademy.org. 29:T45a,A jump discontinuity (or step discontinuity) occurs at $x$-values where the one-sided limits exist but aren't real. [[graph 1]] Looking at the graph we can see that $\lim\limits_{x \to -1^{\bm{-}}} f(x) = -1$ while $\lim\limits_{x \to -1^{\bm{+}}} f(x) = -6$. Therefore, $f$ has a jump discontinuity at $x= -1$. $f$ has removable discontinuities at $x = -6$ and at $x=4$. So these answers are incorrect. **In conclusion, $x=-1$ is the only value where $f$ has a jump discontinuity.** --- Licensing information: The question comes from Khan Academy, and is licensed under a creative commons license. The original exercise containing this question can be found here: Classify discontinuities. Note: All Khan Academy content is available for free at www.khanacademy.org. 2a:T435,A jump discontinuity (or step discontinuity) occurs at $x$-values where the one-sided limits but aren't equal. [[graph 1]] Looking at the graph we can see that $\lim\limits_{x \to -2^{\bm{-}}} f(x) = 0$ while $\lim\limits_{x \to -2^{\bm{+}}} f(x) =