How do I find the modulus of a function?

• How do I solve modulus equations graphically?

• To solve |f(x)| =?g(x) graphically
  • Draw?y?= |f(x)| and?y?=?g(x) into your GDC
  • Find the?x-coordinates of the?points of intersection

How do I solve modulus equations analytically?

• To solve |f(x)| =?g(x) analytically
  • Form?two equations
    • f(x) =?g(x)
    • f(x) = -?g(x)
  • Solve both equations
  • Check solutions?work in the original equation

How do I solve modulus inequalities analytically?

• To solve?any?modulus inequality
  • First solve the corresponding modulus equation
    • Remembering to?check whether solutions are valid
  • Then use a graphical method or a sign table to find the intervals that satisfy the inequality
• Another method is to solve?two pairs of inequalities
  • For |f(x)| <?g(x) solve:
    • f(x) <?g(x) when?f(x) ≥ 0
    • f(x) > -g(x) when?f(x) ≤ 0
  • For |f(x)| >?g(x) solve:
    • f(x) >?g(x) when?f(x) ≥ 0
    • f(x) < -g(x) when?f(x) ≤ 0