Answer
a) A one-to-one function must:
i) have one value for every input
ii) not take the same value for different inputs ($f(x_{1})\ne f(x_{2})$) where $x_{1}\ne x_{2}$
b) Use the horizontal line test: a function is one-to-one if a horizontal line drawn to the graph only intersects the graph at one point.
Work Step by Step
a) The definition of a one-to-one function is a function (i) which never takes on the same value for different inputs (ii).
b) A function is one-to-one if ii) is fulfilled. If ($f(x_{1})\ne f(x_{2})$) where $x_{1}\ne x_{2}$, the same y-value can not occur twice. The horizontal line test verifies this by checking whether the same y-value appears twice on the graph.
