Sketch with |x| in function

Questions where the absolute value is applied to x within the function (e.g., y = (|x|+1)/(|x|-1)) rather than to the entire function output.

1 questions

CAIE Further Paper 1 2022 June Q1
1
  1. Sketch the curve with equation \(\mathrm { y } = \frac { \mathrm { x } + 1 } { \mathrm { x } - 1 }\).
  2. Sketch the curve with equation \(\mathrm { y } = \frac { | \mathrm { x } | + 1 } { | \mathrm { x } | - 1 }\) and find the set of values of x for which \(\frac { | \mathrm { x } | + 1 } { | \mathrm { x } | - 1 } < - 2\).