Check if a linear function or an affine function can be a pseudo random function
Intuitively, pseudorandom functions are functions that look random. A linear function $f$ satisfies
$$ f(x+y) = f(x)+f(y) $$
for all $x,y$, which is highly unlikely for a random function. Similarly, an affine function $f$ satisfies
$$ f(x+y) - f(x+z) = f(y) - f(z) $$
for all $x,y,z$, which is highly unlikely for a random function.