1. The problem is to understand and analyze the function $y = 4\sqrt{x}$.\n\n2. This function represents $y$ as four times the square root of $x$. The square root function $\sqrt{x}$ is defined only for $x \geq 0$ because the square root of a negative number is not a real number.\n\n3. The formula used is $y = 4\sqrt{x}$. Important rules: the domain is $x \geq 0$, and the range is $y \geq 0$ because square roots are non-negative and multiplying by 4 keeps it non-negative.\n\n4. To find some points, substitute values of $x$: \n- For $x=0$, $y=4\sqrt{0}=4\times0=0$.\n- For $x=1$, $y=4\sqrt{1}=4\times1=4$.\n- For $x=4$, $y=4\sqrt{4}=4\times2=8$.\n\n5. The graph starts at the origin $(0,0)$ and increases as $x$ increases, but the growth slows down because the square root function grows slower than linear.\n\n6. The function has no $y$-intercept other than at the origin and no negative $x$ values in its domain.\n\nFinal answer: The function $y=4\sqrt{x}$ is defined for $x \geq 0$ and produces $y \geq 0$, growing as the square root of $x$ multiplied by 4.