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Chapter 1: Problem 84

Determine whether the function is even, odd, or neither. Then describe the symmetry. $$ h(x)=x^{3}-5 $$

Short Answer

Expert verified
The function \( h(x) = x^{3}-5 \) is neither even nor odd, therefore it has no symmetry.

Step by step solution

01

Evaluate \( h(-x) \)

Substitute minus \( x \) into the equation for \( h(x) = x^{3}-5 \) to get \( h(-x) = (-x)^{3}-5 = -x^{3}-5 \). This result is not equal to both \( h(x) \) and \( -h(x) \), so the function is neither even nor odd.
02

Analyze the symmetry

Since the function \( h(x) = x^{3}-5 \) is neither even nor odd, it does not exhibit symmetry with respect to either the y-axis or the origin. It lacks a vertical line of symmetry and rotational symmetry.

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