What does the notation $f\left(x\right)$ represent in the context of functions relating $x$ and $y$?

Given $f\left(x\right)=3x-1$, evaluate $f\left(4\right)$.

Rewrite $y=4x-5$ in function notation as $f\left(x\right)=4x-5$, then find the value of $x$ such that $f\left(x\right)=7$.

A linear function $f$ is known to satisfy $f\left(1\right)=3$ and $f\left(3\right)=7$. Find the constants $a$ and $b$ so that $f\left(x\right)=ax+b$.

A Fahrenheit function is defined by $F\left(C\right)=\frac{9}{5}C+32$. What is $F(-10)$?