Answer:
A function can be described as one-to-one or many-to-one, i.e. each value in the domain ([tex]x[/tex]-values) is mapped to a single value in f(x).
An example of a one-to-one function is a linear function. For every value of x there is one value of y.
An example of a many-to-one function is a quadratic function, where 2 different x-values map to one y-value.
[tex]x^2+y^2=1[/tex] is not a function as some values of [tex]x[/tex] are mapped to two different values of f(x).
For example, let x = 0.5
[tex]\implies (0.5)^2+y^2=1[/tex]
[tex]\implies y^2=0.75[/tex]
[tex]\implies y=\pm\sqrt{0.75}[/tex]
So as x = 0.5 maps to √0.75 and -√0.75, it is one-to-many, and is therefore not a function.
