Question

the square root function
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use the graphing calculator to graph the function f(x) = -√x. which list contains three points that lie on the graph of
the function?
○ (-9, 3), (-4, 2), (-1, 1)
○ (1, 1), (4, 2), (9, 3)
○ (-9, -3), (-4, -2), (-1, -1)
○ (1, -1), (4, -2), (9, -3)
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Explanation:

Step1: Analyze the domain of the function

The function is \( f(x)=-\sqrt{x} \). The square root function \( \sqrt{x} \) is defined for \( x\geq0 \), so the domain of \( f(x) \) is \( x\geq0 \). This means we can eliminate the options with negative \( x \)-values (first and third options).

Step2: Test the remaining options

For the second option \((1,1),(4,2),(9,3)\):

Substitute \( x = 1 \) into \( f(x)=-\sqrt{x} \), we get \( f(1)=-\sqrt{1}=-1
eq1 \). So this option is incorrect.

For the fourth option \((1, - 1),(4,-2),(9,-3)\):

• Substitute \( x = 1 \): \( f(1)=-\sqrt{1}=-1 \), which matches the point \((1,-1)\).
• Substitute \( x = 4 \): \( f(4)=-\sqrt{4}=-2 \), which matches the point \((4,-2)\).
• Substitute \( x = 9 \): \( f(9)=-\sqrt{9}=-3 \), which matches the point \((9,-3)\).

Answer:

D. \((1,-1),(4,-2),(9,-3)\) (assuming the options are labeled A, B, C, D as per the order: A. \((-9,3),(-4,2),(-1,1)\), B. \((1,1),(4,2),(9,3)\), C. \((-9,-3),(-4,-2),(-1,-1)\), D. \((1,-1),(4,-2),(9,-3)\))