Even and odd functions
Answers are for parents and teachers.
1
Decide whether y = x⁶ − x² is even or odd.
even
2
Decide whether y = x⁵ − 2x is even or odd.
odd
3
Show with y(1) and y(−1) that y = x³ + 1 is neither even nor odd.
y(1) = 2, y(−1) = 0; 0 ≠ 2 and 0 ≠ −2
4
For an odd function with y(1) = 3 and y(2) = −1, find y(−1) and y(−2).
y(−1) = −3, y(−2) = 1
5
For x ≥ 0 the graph passes through (1, 2) and (2, 5). Through which points does it pass for x < 0 if the function is even, and if it is odd?
even: (−1, 2), (−2, 5); odd: (−1, −2), (−2, −5)