Which of the following functions has a graph that is symmetric with respect to the origin?

Answer and explanation

Correct answer: C.

  1. Step 1: Symmetry with respect to the origin indicates an odd function: .
  2. Step 2: Test : . Thus it is symmetric with respect to the origin.
  3. Step 3: By comparison, and are even functions (symmetric with respect to the -axis), while has no line or point symmetry.
Answer
.
Why not the others: '' is symmetric with respect to the -axis; '' is an even function; '' is neither even nor odd.

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