I need help with these questions

1. Does there exist a continuous function from (0,1) onto [0,1]

2. Does there exist a continuous function from (-1,1) onto R

3. Does there exist a continuous function from R onto (-1, 1)

4. Does there exist a continuous function from R onto Q

5. Does there exist a continuous function from Q onto R

where R = real numbers

and Q = rational numbers