What does it mean for a "formula to be undefined"?

Question

I was covering the techniques used sketch rational functions of five different types as follows:

However, then I encountered this:

And, Ij just can't find out what it means for the formula to be undefined in this context. Can someone elaborate please, an example would be favourable.

Answer 1

They mean that the formula for some $x$ is undefined, because of division by zero.

Example:

$$\frac{3x^2+5x+6}{x^2-2x+1}$$

If $x=1$, the denominator is 0 and the result is undefined.

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Other possibility: When $d=e=f=0$, the formula is undefined for all $x$.