Functions and their graphs (precalculus)

How is the graph of $y = f(x + 3)$ obtained from the graph of $y = f(x)$?

Let $f(x) = 2x + 1$ and $g(x) = x^2$. Compute $(g \circ f)(2)$.

What is the natural domain of $h(x) = \dfrac{\sqrt{x - 1}}{x - 3}$?

Let $f(x) = \dfrac{x - 1}{x + 2}$ for $x \ne -2$. Which formula gives $f^{-1}(x)$?

Find all vertical asymptotes $x = a$ of $r(x) = \dfrac{x + 1}{x^2 - 1}$. Enter the set of numbers $a$, for example {2, 5}.

Which of these functions are odd, meaning $f(-x) = -f(x)$ for every $x$ in the domain? Choose all that apply.

The function $f(x) = \dfrac{1}{x}$ is strictly decreasing on $(-\infty, 0)$ and on $(0, \infty)$. Which statement is true on its whole domain $x \ne 0$?

Which Lean statement says that the graph of $y = f(x - h)$ is the graph of $f$ moved $h$ units to the right? Here graph f is the set of points (x, f x), and F '' S is the image of the set S under the map F.

Write inverse_value(f, y, lo, hi, steps) that evaluates the inverse of a strictly increasing function f at y by bisection. Assume f(lo) <= y <= f(hi). Repeat steps times: look at the midpoint mid; if f(mid) <= y the answer is in [mid, hi], otherwise in [lo, mid]. Return the midpoint of the final interval.