Review question

# If $y=(x^2+1)/(x^2-a^2)$, then $y$ cannot take which values? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8765

## Suggestion

Show that, if $y=\dfrac{x^2+1}{x^2-a^2}$, $y$ takes all real values twice, except those for which $-\frac{1}{a^2}\le y\le 1$. Sketch the curve $y=\dfrac{x^2+1}{x^2-4}$, indicating its asymptotes.

Could we rearrange the equation into the form $x^2 = f(y)$?

Could we try sketching the graph before answering the first part of the question?