# 2.2  Functions
# Art Belmonte, Summer 1996
# These are the shaded gray examples which appear in Section 2.2.
> restart; f:=x->2*x^3 - 5*x^2 + x + 2;

                                 3      2
                    f := x -> 2 x  - 5 x  + x + 2

> f(6);

                                 260

> f(a+h);

                          3            2
                 2 (a + h)  - 5 (a + h)  + a + h + 2

> vol:=(x,y)->x^2*y; vol(3,5);

                                          2
                        vol := (x, y) -> x  y


                                  45

> plot(f, -2..3); plot(f(x), x=-2..3);
> factor(f(x));

                      (x - 1) (x - 2) (2 x + 1)

> g:=2*x^3 - 5*x^2 + x + 2; factor(g);

                               3      2
                       g := 2 x  - 5 x  + x + 2


                      (x - 1) (x - 2) (2 x + 1)

# Incorrect syntax: Clearly not what we intended!
> factor(g(x));

                  (x(x) - 1) (x(x) - 2) (2 x(x) + 1)

> f:=2*x^3 - 5*x^2 + x + 2;

                               3      2
                       f := 2 x  - 5 x  + x + 2

> f:=unapply(f, x);

                                 3      2
                    f := x -> 2 x  - 5 x  + x + 2

>