Question

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graph: $f(x) = -sqrt{x}$
step 1: evaluate the function to find three points.
$f(0) = 0$
$f(1) = -1$
$f(4) = -2$
step 2: plot the points (0, 0), (1, -1), and (4, -2).

Explanation:

Step 1: Complete the table

We have the points \((0,0)\), \((1, - 1)\) and \((4,-2)\) from evaluating the function \(f(x)=-\sqrt{x}\). So in the table, when \(x = 0\), \(y=0\); when \(x = 1\), \(y=-1\); when \(x = 4\), \(y = - 2\).

\(x\)	\(y\)
\(1\)	\(-1\)
\(4\)	\(-2\)

Step 2: Graph the function

After plotting the points \((0,0)\), \((1,-1)\) and \((4, - 2)\), we draw a smooth curve passing through these points. The domain of \(f(x)=-\sqrt{x}\) is \(x\geq0\), and as \(x\) increases, \(y =-\sqrt{x}\) decreases (since the square - root function \(\sqrt{x}\) is increasing for \(x\geq0\) and we have a negative sign in front). The graph starts at the origin \((0,0)\) and moves downwards to the right, getting closer to the negative \(y\) - axis as \(x\) increases.

Answer:

The table is filled as above, and the graph is a curve passing through \((0,0)\), \((1,-1)\) and \((4,-2)\) with the domain \(x\geq0\) and decreasing for \(x\geq0\).