Hey there!
General tips for graphing \((f(x))^2\) given \(f(x)\):
- Start by drawing \(|f(x)|\) (reflecting all negative parts of \(f(x)\) around the x-axis, since \(\sqrt{ (f(x))^2} = |f(x)|\)
- \((f(x))^2\) will be below \(|f(x)|\) where \(|f(x)| < 1\), and \((f(x))^2\) will be above \(|f(x)|\) where \(|f(x)| > 1\)
- \((f(x))^2\) will always be greater than 0 for all x in the domain of \(|f(x)|\)
- Turn all cusps formed by \(|f(x)|\) into smooth turning points (like on a parabola)
- Keep all vertical asymptotes
- Square all horizontal asymptotes (move them accordingly)
- Indicate clearly the slope of \((f(x))^2\) - \(\frac{d}{dx} (f(x))^2 = 2f'(x)f(x)\).
Can't think of anything else atm, but hope this is enough to get you started