Recognizing features of functions (example 2) | Algebra II | Khan Academy

TL;DR

Given three functions, f(x), g(x), and h(x), only h(x) is odd.

Transcript

Which of these functions is odd? And so let's remind ourselves what it means for a function to be odd. So I have a function-- well, they've already used f, g, and h, so I'll use j. So function j is odd. If you evaluate j at some value-- so let's say j of a. And if you evaluate that j at the negative of that value, and if these two things are the ne... Read More

Key Insights

• 🦕 In order for a function to be odd, evaluating it at a value and its negative counterpart should give opposite results.
• 🦕 The functions f(x) and g(x) are not odd because they do not meet this criterion.
• 🦕 The function h(x) is odd because evaluating it at a value and its negative counterpart gives opposite results.
• 🦕 Odd functions are symmetric around the origin.
• 🦕 Flipping an odd function over both axes results in the same function.

Questions & Answers

Q: What does it mean for a function to be odd?

A function is odd if evaluating it at a value and its negative counterpart gives opposite results. This means that if f(x) = y, then f(-x) = -y.

Q: Is f(x) odd?

No, f(x) is not odd. Evaluating f(x) at a particular value and its negative counterpart does not give opposite results.

Q: Is g(x) odd?

No, g(x) is not odd. Evaluating g(x) at any value and its negative counterpart gives the same result.

Q: Is h(x) odd?

Yes, h(x) is odd. Evaluating h(x) at a value and its negative counterpart gives opposite results, satisfying the criteria for oddness.

Summary & Key Takeaways

• A function is odd if evaluating it at a value and its negative counterpart gives opposite results.

• f(x) is not odd because f(x) and f(-x) do not have opposite values.

• g(x) is not odd because g(x) and g(-x) have the same values.

• h(x) is odd because h(x) and h(-x) have opposite values.