Question

this table defines function f:
x | -2 | -1 | 0 | 1 | 2
f(x) | -3 | -2 | 0 | 2 | 3
according to the table, is f even, odd, or neither?
choose 1 answer:
a even
b odd
c neither

Explanation:

Step1: Recall odd function definition

An odd function satisfies $f(-x) = -f(x)$ for all $x$.

Step2: Check $x=1$

$f(-1) = -2$, $-f(1) = -2$. So $f(-1)=-f(1)$.

Step3: Check $x=2$

$f(-2) = -3$, $-f(2) = -3$. So $f(-2)=-f(2)$.

Step4: Check $x=0$

$f(-0)=f(0)=0$, $-f(0)=0$. So $f(-0)=-f(0)$.

Step5: Conclusion

All $x$ satisfy $f(-x)=-f(x)$, so $f$ is odd.

Answer:

B. Odd