Question

determine whether the function is even, odd, or neither.

\\f(x) = 6x^6 + 2x^2 + |x|\\

• the function is an even function.
• the function is an odd function.
• the function is neither even nor odd.

Explanation:

State the given function and definitions

Using the Even and Odd Functions knowledge point

$$
LATEXBLOCK0
$$

Evaluate the function at negative x

Using the Function Evaluation knowledge point

$$ f(-x) = 6(-x)^6 + 2(-x)^2 + |-x| $$

Simplify the expression

Using the Absolute Value Properties knowledge point

$$
LATEXBLOCK1
$$

Answer:

• The function is an even function. (Correct answer)
• The function is an odd function.
• The function is neither even nor odd.