Quick questions on Functions, domain and range explained: H2 Mathematics Functions and Graphs

A relation in the $x$-$y$ plane defines $y$ as a function of $x$ exactly when every vertical line $x = c$ meets the graph at most once. If some vertical line meets it twice, one input has two outputs and the relation is not a function. A circle and the sideways parabola $y^2 = x$ both fail this test.

To find the range of $\mathrm{f}$ on a stated domain:

State what is meant by a function and by a one-to-one function. [2 marks]

The function $\mathrm{f}$ is defined by $\mathrm{f}(x) = (x + 1)^2 - 5$ for $x \geq -1$. Find the range and state whether $\mathrm{f}$ is one-to-one. [3 marks]

Explain why the relation $x^2 + y^2 = 4$ does not define $y$ as a function of $x$. [2 marks]