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:T538,For a function to be continuous over an entire interval, it has to be continuous on every point in that interval. Graphically, this is roughly the same as being able to draw the graph of the function on that interval without lifting the pencil. [[graph 1]] $\lim\limits_{x \to 3^{\bm{-}}} f(x) \not= f(3)$ because $f(3)$ isn't defined. Therefore, $f$ isn't continuous at $x=3$. Since $f$ isn't continuous on one of the points in $[-1,3]$, it isn't continuous over that interval. [[graph 2]] The one-sided limit $\lim\limits_{x \to 3^{\bm{-}}} g(x)$ does exist and equals $g(3)$. The graph of $g$ seems to be continuous over $[-1,3]$. **In conclusion, only $g$ is continuous over the interval $[-1,3]$**. --- 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: Continuity over an interval. Note: All Khan Academy content is available for free at www.khanacademy.org. 28:T513,For a function to be continuous over an entire interval, it has to be continuous on every point in that interval. Graphically, this is roughly the same as being able to draw the graph of the function on that interval without lifting the pencil. [[graph 1]] The value $g(0)$ is undefined, so $g$ isn't continuous at $x=0$. Since $g$ isn't continuous on one of the points in $[-2,0]$, it isn't continuous over that interval. $\lim\limits_{x \to 3} g(x) \not= g(3)$. Therefore, $g$ isn't continuous at $x=3$. Since $g$ isn't continuous on one of the points in $[1,5]$, it isn't continuous over that interval. **In conclusion, $g$ is not continuous over either interval.** --- 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: Continuity over an interval. Note: All Khan Academy content is available for free at www.khanacademy.org. 29:T4fd,For a function to be continuous over an entire interval, it has to be continuous on every point in that interval. Graphically, this is roughly the same as being able to draw the graph of the function on that interval without lifting the pencil. [[graph 1]] The one-sided $\lim\limits_{x \to -1^{\bm{+}}} f(x)$ exists and equals $f(-1)$. Therefore, $f$ is continuous over the interval $[-1,4]$. $\lim\limits_{x \to -5} f(x)$ doesn't exist, so $f$ isn't continuous at $x=-5$. Since $f$ isn't continuous on one of the points in $[-5, -2]$, it isn't continuous over that interval. **In conclusion, $f$ is only continuous over the interval $[-1, 4]$.** --- 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: Continuity over an interval. Note: All Khan Academy content is available for free at