Domains, intervals and piecewise values by hand

The domain of $f(x) = \sqrt{x - 5}$ is a single interval. Give the number at its left end.

The domain of $f(x) = \sqrt{2x - 8}$ is a single interval. Give the number at its left end.

How many separate intervals does the domain of $g(x) = \dfrac{1}{x^2 - 9}$ need?

Give the larger of the two inputs missing from the domain of $h(x) = \dfrac{x + 1}{x^2 - 4}$.

With $f(x) = 3x$ and $g(x) = x - 7$, which single input is missing from the domain of $\dfrac{f}{g}$?

With $f(x) = \sqrt{x - 4}$ and $g(x) = x + 1$, the domain of $f \circ g$ is a single interval. Give the number at its left end.

With $f(x) = \sqrt{x}$ and $g(x) = x - 10$, the domain of $f \circ g$ is a single interval. Give the number at its left end.

With $f(x) = \dfrac{1}{x}$ and $g(x) = x - 6$, which single input is missing from the domain of $f \circ g$?

$f$ has domain $[2, \infty)$ and $g$ has domain $(-\infty, 6]$. The domain of $fg$ is $[2, b]$. Give $b$.

The domain of $f(x) = \sqrt{x} + \dfrac{1}{x - 2}$ starts at one number and has one number removed from it. Give the number that is removed.

For the rule that is $2x + 3$ when $x < 1$ and $x^2$ when $x \ge 1$, find $f(1)$.

For that same rule, find $f(0.5)$.

For that same rule, find $f(3)$.

Find $\lfloor -2.3 \rfloor$.

Find $\lceil 4.01 \rceil$.

A car park charges 3 pounds for each started hour. What does a stay of 2.2 hours cost, in pounds?

Postage is $C(w) = 2$ for $0 < w \le 100$, $C(w) = 5$ for $100 < w \le 500$, and $C(w) = 9$ for $w > 500$. Find $C(500)$.

For that same postage rule, find $C(501)$.

Function $S$ has the values $S(0) = 7$, $S(2) = 11$, $S(4) = 15$. Give its rate of change per unit of input.

For that same table, assuming the pattern continues, give $S(10)$.