If $f$ is a continuous real-valued function defined on a closed interval $[a, b]$,then the range of the function is . . . . . .

If $f(x) = \frac{x^2 - bx + 25}{x^2 - 7x + 10}$ for $x \neq 5$ and $f$ is continuous at $x = 5$,then the value of $f(5)$ is:

The number of points of discontinuity of the function $f(x) = \frac{1}{1 - e^{\frac{-x-1}{x-2}}}$ is

Find the relationship between $a$ and $b$ so that the function $f$ defined by $f(x) = \begin{cases} ax + 1, & \text{if } x \le 3 \\ bx + 3, & \text{if } x > 3 \end{cases}$ is continuous at $x = 3$.

If $f(x) = |x - b|,$ then the function:

Find the values of $k$ so that the function $f$ is continuous at the indicated point.
$f(x) = \begin{cases} \frac{k \cos x}{\pi - 2x}, & \text{if } x \neq \frac{\pi}{2} \\ 3, & \text{if } x = \frac{\pi}{2} \end{cases}$ at $x = \frac{\pi}{2}$