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

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 \(x\geq0\).

分类: calculus 更新时间: 2026-02-06

题目

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).

解题步骤

  1. 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).

  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.

  3. 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 \(x\geq0\).

答案

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 \(x\geq0\).

Question Image

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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

Show OCR extraction 
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).

相关知识点

mathematicscalculuswith charthigh schoolliked-answerturns-1

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