Which of the following may be correctly expressed by the graph represe

\(?\,\,\,:\,\,\,{\rm{graph}}\,\,{\rm{association}}\)

From the figure given:

> We expect y to decrease whenever |x| increases, in other words, whenever x > 0 gets larger or x < 0 gets smaller (i.e., more negative).
> This is enough to refute (A) and (B).

> We expect y to be defined for all values of x, except when x is zero.
> This is enough to refute (C): when x < 0, x^(-1/2) is not defined.

> We expect y to be positive for all nonzero values of x.
> This is enough to refute (D): when x<0, x^(-1) is negative.

The correct answer is therefore (E), by exclusion!

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

P.S.: more quantitative mature students may also take into account the symmetry related to the y-axis, in the sense that we expect f(x) = f(-x) ...