Question
What type of function is \( f(x)=-5 x^{3} \) ? Option \#1: even Option \#2: odd Option \#3: neither (1 point)
Ask by Griffin Watson. in the United States
Jan 23,2025
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Tutor-Verified Answer
Answer
The function \( f(x) = -5x^3 \) is **odd**.
Solution
The function \( f(x) = -5x^3 \) is **odd**.
**Explanation:**
- A function is **odd** if \( f(-x) = -f(x) \).
- For \( f(x) = -5x^3 \):
\[
f(-x) = -5(-x)^3 = -5(-x^3) = 5x^3 = -(-5x^3) = -f(x)
\]
- Since \( f(-x) = -f(x) \), the function is odd.
**Answer:**
Option #2: odd
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Simplify this solution Extra Insights
The function \( f(x)=-5 x^{3} \) is an odd function. This is because if you substitute \( -x \) into the function, you get \( f(-x) = -5(-x)^3 = 5x^3 = -f(x) \). Since it satisfies the property of odd functions, we can confidently say it falls under this category. To visualize it, graphing \( f(x)=-5 x^{3} \) will showcase symmetry about the origin. As you move in one direction along the x-axis, the function produces the negative of its value in the opposite direction, confirming its odd nature!
