find the y-intercept and zeros of f(x)=$$ ^3\sqrt{x} $$

To find the $ y $-intercept and the zeros of the function $ f(x) = \sqrt[3]{x} $, let's follow these steps:

### 1. **Finding the $ y $-Intercept:**

The $ y $-intercept occurs when $ x = 0 $. Substituting $ x = 0 $ into the function:

\[
f(0) = \sqrt[3]{0} = 0
\]

So, the $ y $-intercept is $ (0, 0) $.

### 2. **Finding the Zeros:**

The zeros of the function occur when $ f(x) = 0 $. We set the function equal to zero and solve for $ x $:

\[
\sqrt[3]{x} = 0
\]

To eliminate the cube root, cube both sides:

\[
x = 0
\]

So, the function has a zero at $ x = 0 $.

### Summary:
- **$ y $-intercept:** $ (0, 0) $
- **Zeros:** $ x = 0 $

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. What is the domain of $ f(x) = \sqrt[3]{x} $?
2. How does the graph of $ f(x) = \sqrt[3]{x} $ compare to $ f(x) = \sqrt{x} $?
3. What are the transformations of $ f(x) = \sqrt[3]{x + 2} $?
4. What is the slope of the tangent line to $ f(x) = \sqrt[3]{x} $ at $ x = 1 $?
5. Find the zeros of the function $ g(x) = \sqrt[3]{x - 4} $.

**Tip:** Unlike square roots, cube roots can take any real number, including negative numbers, and they have no restrictions on their domain.

Discover how to find the y-intercept and zeros of the function f(x) = cube root of x with detailed step-by-step instructions. Learn about cube roots and their properties in this high school-level math problem.

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