Question

consider the following function.
r(x)=-\frac{7sqrt{x}}{9}
step 1 of 2: identify the general shape of the graph of this function.
answer

Explanation:

Step1: Recall square - root function properties

The general form of a square - root function is $y = a\sqrt{x}+b$. Here, $a =-\frac{7}{9}$ and $b = 0$. The domain of $r(x)=-\frac{7\sqrt{x}}{9}$ is $x\geq0$ since we cannot take the square root of a negative number in the real - number system.

Step2: Analyze the coefficient of $\sqrt{x}$

The coefficient $a =-\frac{7}{9}<0$. For a square - root function $y = a\sqrt{x}+b$, when $a>0$, the graph starts at the origin $(0,0)$ and increases as $x$ increases. When $a < 0$, the graph starts at the origin $(0,0)$ and decreases as $x$ increases.

Answer:

The graph starts at the origin $(0,0)$ and is a decreasing curve for $x\geq0$.