For the described function, check for continuity:

$c\left(t\right)$: cost of admission to a museum on day $t$ of the year

Find the interval of continuity for function. Also, identify the endpoints for which the function is left-continuous or right-continuous.

$g\left(x\right)=\sqrt{289-x^2}$

A cyclist leaves their home for a $3$-hour ride to a park on a Saturday morning at $8$ A.M. The park is $9$ miles away from their home. On a Monday morning, they cycle back home from the park, starting at $8$ A.M. and taking the same $3$ hours. Let $p\left(t\right)$ be the cyclist's distance from home $t$ hours after $8$ A.M. on Saturday, and $q\left(t\right)$ be the distance from home $t$ hours after $8$ A.M. on Monday. If $r\left(t\right)=p\left(t\right)-q\left(t\right)$, what are $r\left(0\right)$ and $r\left(3\right)$?

A coffee shop charges for Wi-Fi access based on the time used. The graph of the charge function $c$ for $0\le t\le 40$ is given below. Write the intervals of continuity of $c$.

On what interval is the following function continuous?

$g\left(x\right)=\frac{1}{x+3}$

Consider the graph of the given function $g\left(x\right)$. What is the value of $\underset{x\to -2^{+}}{\lim }g\left(x\right)$?

For the function $f\left(x\right)$ given by , find the values of $c$ and $d$ that make it continuous everywhere.