Question

State whether the following statements are true or false. Justify yourself with the help of a short proof or a counter example. (3) The graph of every function from [0, 1] to R is infinite

Answer 1

The statement is false .

We have many counter example.

1.Define a function,

$f:[0,1]\rightarrow R$ , by $f(x)=5$

Which is a constant function and is finite.

2.$f:[0,1]\rightarrow R$ defined by $f(x)=x$

Which is a bounded function ,bounded by 5. Etc