graph the function.\ny = -\\frac{3}{2}\\sqrt{x}\nclick to plot points on the graph. plot the endpoint first.

Explanation:

Step1: Determine the domain

The expression under the square - root must be non - negative. So, $x\geq0$. The domain of the function $y =-\frac{3}{2}\sqrt{x}$ is $[0,+\infty)$. The endpoint is when $x = 0$. When $x = 0$, $y=-\frac{3}{2}\sqrt{0}=0$. So the endpoint is the point $(0,0)$.

Step2: Choose other values of x

Let's choose $x = 1$. Then $y=-\frac{3}{2}\sqrt{1}=-\frac{3}{2}$. Let's choose $x = 4$. Then $y=-\frac{3}{2}\sqrt{4}=-\frac{3}{2}\times2=-3$.

Step3: Plot the points

Plot the endpoint $(0,0)$ first. Then plot the points $(1,-\frac{3}{2})$ and $(4, - 3)$. Connect the points with a smooth curve. Since the domain is $x\geq0$, the curve starts at the origin $(0,0)$ and extends to the right in the fourth quadrant (because the coefficient of $\sqrt{x}$ is negative).

Answer:

Plot the points $(0,0)$, $(1,-\frac{3}{2})$, $(4,-3)$ and connect them with a smooth curve for $x\geq0$.