graph: $f(x) = -sqrt{x}$ step 1: evaluate the function to find three po…

Question

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).

Solution Steps

Understand the question
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 $x = 4$, $y = - 2$.
| $x$ | $y$ |
|-------|-------|
| $0$ | $0$ |
| $1$ | $-1$ |
| $4$ | $-2$ |

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.
Final 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 $x\geq0$.

Answer

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 $x = 4$, $y = - 2$.
| $x$ | $y$ |
|-------|-------|
| $0$ | $0$ |
| $1$ | $-1$ |
| $4$ | $-2$ |

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 $x\geq0$.

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Question Analysis

Subject mathematics

Sub Subject calculus

Education Level high school

Difficulty unspecified

Question Type with chart

Multi Question No

Question Count 1

Analysis Status completed

Analyzed At 2026-02-06T15:15:53

OCR Text

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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).

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