Question

on which of the following intervals is ( j(x) ) increasing?
( -1 < x < 1 )

Explanation:

Step1: Analyze the function values

When \(x=-1\), \(j(x) = 1\); when \(x = 0\), \(j(x)=4\); when \(x = 1\), \(j(x)=5\).
We can see that as \(x\) increases from \(-1\) to \(1\) (\(-1

Step2: Check other intervals (for completeness)

For \(x\) from \(1\) to \(2\): \(j(1) = 5\), \(j(2)=4\) (function is decreasing).
For \(x\) from \(2\) to \(3\): \(j(2) = 4\), \(j(3)=1\) (function is decreasing).
For \(x\) from \(3\) to \(4\): \(j(3) = 1\), \(j(4)=-4\) (function is decreasing).
For \(x\) from \(4\) to \(5\): \(j(4) = -4\), \(j(5)=-11\) (function is decreasing).

Answer:

\(-1 < x < 1\)