Function Rule of a table

Question

Can we write the function rule as for example $2x+3$ instead of $y=2x+3$? Is it right mathematically or not?

Answer 1

It's right mathematically as long as it's clear to the audience what you're talking about. Here, I know what you mean when you say "consider the function $2x+3$," "consider the function $y=2x+3$" or "consider the function $f(x) = 2x+3.$" You mean the function that takes a real number $x$ and spits out $2x+3.$ Did you actually mean the complex numbers or the integers? I'd guess not since you used $x$ instead of $z$ or $n.$ Did you actually mean positive reals? Harder to say here, but that's not usually the case with $2x+3.$

For complete precision (which is important when it's not as clear from context), you'd want to also give a domain and range. For instance "consider the function $f:\mathbb R\to \mathbb R$ defined by the rule $f(x) = 2x+3".$

People will say "$2x+3$ is an expression, not a function," and they aren't wrong, but again, in this situation it's usually clear.

However, if I'm gonna be picky, I prefer "$f(x) = 2x+3$" or "$y(x) = 2x+3$" to "$y=2x+3$" or just "$2x+3$" because it's clear you're considering a function with argument $x$ called $f$ (or $y$).

EDIT On looking at the title, I see it is 'function rule of a table.' Although I claimed to know exactly what you meant by $2x+3,$ I have no idea what you meant by 'table'. Perhaps I should have been more of a stickler for precision in my answer.

Answer 2

You need to give the $2x + 3$ the connection to functions. It is not clear per se that $x$ is the argument of a function.

While $2 \,\text{id} + 3$ would be clearly a function.