Question

Given the graph of the function `y=f(x)`, draw the graph of `y ="sgn"(x)`.

Answer 1

From the graph, `f(x) gt 0` for ` x lt -3 or x gt 1 `
`therefore " ""sgn"(f(x))= 1` for `x in (-oo, -3) uu ( 1, oo)`
`" "f(x) lt 0` for `x in (-3, 1)`
`therefore" ""sgn"(f(x)) = -1 ` for `x in (-3, 1)`
`" "f(x) =0` for `x= -3, 1`
`therefore " " "sgn (f(x))= 0` for `x = -3, 1`
Hence the graph of `y="sgn"(f(x))` is as shown in the following figure.