Question

this table defines function $f$:

$x$	$-6$	$-3$	$0$	$3$	$6$

according to the table, is $f$ even, odd, or neither?
choose 1 answer:
a even
b odd
c neither

Explanation:

Step1: Recall definitions

A function \( f \) is even if \( f(-x) = f(x) \) for all \( x \) in the domain. A function \( f \) is odd if \( f(-x) = -f(x) \) for all \( x \) in the domain.

Step2: Check each \( x \)

• For \( x = 6 \): \( f(6) = -4 \), \( f(-6) = -8 \). \( f(-6)

eq f(6) \) (so not even) and \( f(-6)
eq -f(6) \) (since \( -f(6) = 4 \), not -8).

• For \( x = 3 \): \( f(3) = -8 \), \( f(-3) = -4 \). \( f(-3)

eq f(3) \) and \( f(-3)
eq -f(3) \) (since \( -f(3) = 8 \), not -4).

• For \( x = 0 \): \( f(0) = 0 \), \( f(-0)=f(0)=0 \), but other \( x \) values don't satisfy even or odd.

Since for \( x = 3, 6 \), neither \( f(-x)=f(x) \) nor \( f(-x)=-f(x) \) holds, the function is neither.

Answer:

C. Neither