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Term 1 · Weeks 9–10 · Functions and Their Graphs

Challenge problem

Challenge

Find the sum of the xx-intercepts of f(x)=∣x−2∣−3f(x) = |x - 2| - 3.

Show step-by-step solution

Answer: 4

  1. Set f(x)=0f(x) = 0: ∣x−2∣=3|x - 2| = 3.
  2. So x−2=3x - 2 = 3 or x−2=−3x - 2 = -3, giving x=5x = 5 or x=−1x = -1.
  3. Sum: 5+(−1)=45 + (-1) = 4.

Common errors to watch for

  • Finding only one intercept (x=5x = 5).

Budget of Work competencies

  • gm11.t1.w10.c1
    Sketch the graph of the following functions: linear, absolute value, quadratic, square root, or cube root with or without technology.

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