Question

Draw the graph of `y= -sqrt(x^(2)+2)`

Answer 1

We have `y= -sqrt (x^(2) +2)`
or `" "y^(2)= x^(2) + 2`
or `" "x^(2) - y^(2)= -2`, which is a rectangular hyperbola.
But `" "y= -sqrt(x^(2) + 2) le 0`
So the graph of `y= f(x)` is part of the hyperbola `x^(2)-y^(2) =-2`, which lies below the x-axis.