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Cogito

AP Precalculus · Chapter 2 · Lesson 2

Practice Worksheet

Even and Odd Functions

Two kinds of symmetry, and the many functions with neither.

11 problems · about 20 minutes · AP Precalculus 1.8

NameDate

Figure — use these to answer the problems

Set b and c to zero to leave x³ alone, which is odd.
-8-8-6-6-4-4-2-222446688
y = 1x³ + 0x + 0
a1
b0
c0
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. f is odd and f(2) = −5. What is f(−2)?

    Answer

  2. x². 1 for even, 2 for odd, 0 for neither.

    Answer

  3. x⁵. 1 for even, 2 for odd, 0 for neither.

    Answer

  4. x² + 3. 1 for even, 2 for odd, 0 for neither.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. x³ + 1. 1 for even, 2 for odd, 0 for neither.

    Answer

  2. Sort each function by its symmetry.

    Write each item under the heading it belongs to: x⁶ · x⁷ · x² + x · cos x · sin x

    Even

    Odd

    Neither

  3. If f is odd, what must f(0) be?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. f is even and f(3) = 7. What is f(−3)?

    Answer

  2. f is odd and f(3) = 7. What is f(−3)?

    Answer

  3. The Test

    Is f(x) = x⁴ even, odd, or neither? Answer 1 for even, 2 for odd, 0 for neither.

    Answer

  4. The Other One

    Is f(x) = x³ − x even, odd, or neither? Answer 1 for even, 2 for odd, 0 for neither.

    Answer