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The problem is asking you to compute \( f(-x) \) and compare it with \( -f(x) \) to determine whether the function is even, odd, or neither.

Given:
\[
f(x) = x^5 - 3x^3
\]

### Step 1: Find \( f(-x) \)
To find \( f(-x) \), substitute \( -x \) into the function:
\[
f(-x) = (-x)^5 - 3(-x)^3
\]
Simplify:
\[
f(-x) = -x^5 - 3(-x^3) = -x^5 + 3x^3
\]

### Step 2: Find \( -f(x) \)
Now, compute \( -f(x) \):
\[
-f(x) = -(x^5 - 3x^3) = -x^5 + 3x^3
\]

### Step 3: Compare \( f(-x) \) and \( -f(x) \)
We see that:
\[
f(-x) = -f(x)
\]

This means that the function is **odd**.

### Fill in the blanks:
- \( f(-x) = -x^5 + 3x^3 \)
- \( -f(x) = -x^5 + 3x^3 \)

Both results are the same, confirming that the function is odd.

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Do you want more details on how to identify even and odd functions or have any other questions?

Here are five related questions to expand on this:
1. How do you determine if a function is even?
2. Can a function be neither even nor odd? How can you tell?
3. What are some common properties of odd functions?
4. Can a polynomial of any degree be odd? Why or why not?
5. How does the symmetry of a graph relate to whether the function is even or odd?

**Tip:** For odd functions, the graph is symmetric about the origin, meaning if you rotate the graph 180 degrees, it looks the same.

Learn how to find f(-x) and -f(x) to determine if the polynomial function f(x) = x^5 - 3x^3 is odd. Step-by-step solution included, covering key algebra concepts for students in Grades 10-12.

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