Question

which of the following is a graph of $f(x)=3 - sqrt{x}$?

Explanation:

Step1: Analyze domain

The function $f(x)=3 - \sqrt{x}$ is defined for $x\geq0$ since we cannot take the square - root of a negative number in the real - number system.

Step2: Analyze y - intercept

When $x = 0$, $f(0)=3-\sqrt{0}=3$. So the y - intercept is at the point $(0,3)$.

Step3: Analyze behavior as x increases

As $x$ increases, $\sqrt{x}$ increases. Since $f(x)=3 - \sqrt{x}$, as $\sqrt{x}$ increases, $f(x)$ decreases. The function is a decreasing function for $x\geq0$.

Answer:

The graph that has a y - intercept at $(0,3)$ and is decreasing for $x\geq0$ among the given options. (Since the options are not labeled, you would need to identify the graph with these characteristics from the ones provided.)