$$ f(x)=5\surd(x),\text{ } $$draw the graph

To draw the graph of the function $ f(x) = 5\sqrt{x} $, let's first analyze the function:

### Key Points:
1. **Domain**: The square root function $ \sqrt{x} $ is only defined for $ x \geq 0 $, so the domain of $ f(x) $ is $ [0, \infty) $.
2. **Shape**: The function represents a vertically stretched square root function by a factor of 5. Since $ \sqrt{x} $ is an increasing function, $ f(x) $ will also be increasing.
3. **Intercept**: At $ x = 0 $, $ f(0) = 0 $, so the graph passes through the origin $ (0, 0) $.
4. **Behavior**: As $ x $ increases, $ f(x) $ will increase more gradually because of the square root function.

Now, let's proceed to plot the graph.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, here’s what the graph of $ f(x) = 5\sqrt{x} $ would look like:

- It starts at the origin (0, 0).
- The curve increases as $ x $ increases, but at a decreasing rate (since it's a square root).
- The graph is confined to the right half of the coordinate plane, as the function is only defined for $ x \geq 0 $.

If you'd like to explore further or have specific questions, feel free to ask!

### Here are 5 related questions:
1. How does the graph of $ f(x) = 5\sqrt{x} $ compare to $ f(x) = \sqrt{x} $?
2. How would the graph change if the function were $ f(x) = 2\sqrt{x} $?
3. Can you find the derivative of $ f(x) = 5\sqrt{x} $?
4. What is the domain and range of $ f(x) = 5\sqrt{x} $?
5. How does the function behave as $ x \to \infty $?

### Tip:
For any square root function $ f(x) = a\sqrt{x} $, increasing the value of $ a $ stretches the graph vertically, making the curve steeper.

Explore how to graph the function f(x) = 5√(x). This problem covers the domain and range of square root functions, and the impact of vertical stretching. Suitable for students in Grades 9-11.

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