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.