Maths - Sketching Graphs

If the coefficient of $x^3$ is positive, how does a cubic graph look?

If the coefficient of $x^3$ is negative, how does a cubic graph look?

A cubic equation has roots $-1, 2$ and $3$. Visualise it’s graph?

What does a graph of $\frac{1}{x}$ look like?

What does a graph of $\frac{1}{x^2}$ look like?

What does a graph of $\frac{-2}{x}$ look like?

What does a graph of $\frac{-5}{x^2}$ look like?

What does a graph of $2^x$ look like?

What does a graph of $\sqrt{x}$ look like?

What does a graph of $\frac{1}{2}^x$ look like?

Rather than sketching

what’s a much easier way of showing that $f(x)$ only has one root?