The word **function** in calculus refers to something like $f(x) = x^2+2x^3$ or $f(x) =\sin(x) $ etc....

In linear algebra, the word **function** is used like-
**A linear transformation is a function from $V \rightarrow W$.**

And the **functions** of calculus like $f(x) = x^2+2x^3$ or $f(x) =\sin(x) $ etc. are actually vectors in either a polynomial space ($f(x) = x^2+2x^3$ ) or a Function space ( like $f(x) =\sin(x) $ ) .

Now the word **function** in Linear Algebra is used twice as I showed above.

So according to me the **functions** of calculus are just vectors in linear algebra. **Is this correct or not.**

But then what are the **functions** being used in the definition of Linear Transformations. And how are they different from the **functions** of calculus and the **functions** which are vectors in linear algebra.

*Edit:*

**Why is the graph of a linear transformation from any vector space to any other vector space not always a straight line. Can anyone give any counter examples.**