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

Challenge problem · non-routine

Challenge Non-routine

A student claims the domain of g(x)=x+53−8g(x)=\sqrt[3]{x+5}-8 is x≥−5x\ge -5. State the correct domain in interval notation.

Show step-by-step solution

Answer: (-∞, ∞)

  1. A cube root is defined for every real number, unlike a square root.
  2. So x+5x+5 may be any real number and the domain is (−∞,∞)(-\infty,\infty).

Common errors to watch for

  • Applying the square-root restriction (radicand ≥0\ge 0) to a cube root.

Budget of Work competencies

  • gm11.t1.w9.c2
    Classify functions based on their graphs and/or equations to determine if they are linear, absolute value, quadratic, square root, or cube root.

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