Thread: Mapping onto

A mapping f: R map element of R is onto iff each horizontal line( line parallel to the x-axis). Intersect the graph of f at least once.

a. Formulate similar condirion for f : R map element of R is one-to one mapping.

B. If both are one to one mapping and onto.

There's a certain symmetry to this question.

Hint: consider vertical lines.

I guess vertical lines would tell me something about whether the function is well-defined or not, but can't see how they help with a) or b).

For a) ask yourself what does it mean when a horizontal line intersects the graph more than once

For b) just combine the statement about 'onto' with what you find in a).