The expression "function rule" means the expression that turns an input into an output.
If the input is 'x' and the output is 'f(x)', the function rule is the "body" of the function.
For example:
[tex]f(x)=x\cdot2+3[/tex]The function rule would be the "*2 + 3", that is applied in the input x so it becomes the output f(x).
