Mastering Mathematics Smartly by Wee Wen Shih

It is typical to ask for a range of values that a given graph y = f (x), where f (x) is a rational function, does not lie in.

These steps will be necessary:

(1) Form a quadratic equation that involves x.

(2) Consider the discriminant to be greater than or equal to 0.

(3) Solve the resulting inequality that involves y.

You can then verify your answers with a graphic calculator.

See example.

Try this!

This is a nice question from a discussion on SgForums in which the graphical approach is superior to the algebraic approach of considering the discriminant.

This diagram shows that  and  each intersects the curve twice.