Math Problem Statement

Use the graphing calculator to graph the function f(x) = -√x. Which list contains three points that lie on the graph of the function?

Solution

To solve this problem, we need to understand the function given: f(x)=xf(x) = -\sqrt{x}. This function is defined only for x0x \geq 0 because the square root of a negative number is not defined in the real number system.

For each of the given points (x,y)(x, y), we will check if the yy-value matches f(x)f(x).

Step-by-step evaluation:

  1. f(x)=xf(x) = -\sqrt{x} means we find the square root of xx and take its negative.

  2. We'll evaluate the function for the provided options:

    • Option A: (9,3),(4,2),(1,1)(-9, 3), (-4, 2), (-1, 1)

      • 9\sqrt{-9} is not defined in the reals.
      • 4\sqrt{-4} is not defined in the reals.
      • 1\sqrt{-1} is not defined in the reals.
      • None of these points are valid.
    • Option B: (1,1),(4,2),(9,3)(1, 1), (4, 2), (9, 3)

      • For (1,1)(1, 1): f(1)=1=1f(1) = -\sqrt{1} = -1, not 11.
      • For (4,2)(4, 2): f(4)=4=2f(4) = -\sqrt{4} = -2, not 22.
      • For (9,3)(9, 3): f(9)=9=3f(9) = -\sqrt{9} = -3, not 33.
      • None of these points are valid.
    • Option C: (9,3),(4,2),(1,1)(-9, -3), (-4, -2), (-1, -1)

      • 9\sqrt{-9}, 4\sqrt{-4}, and 1\sqrt{-1} are not defined in the reals.
      • None of these points are valid.
    • Option D: (1,1),(4,2),(9,3)(1, -1), (4, -2), (9, -3)

      • For (1,1)(1, -1): f(1)=1=1f(1) = -\sqrt{1} = -1.
      • For (4,2)(4, -2): f(4)=4=2f(4) = -\sqrt{4} = -2.
      • For (9,3)(9, -3): f(9)=9=3f(9) = -\sqrt{9} = -3.
      • All three points match.

Conclusion:

Option D: (1,1),(4,2),(9,3)(1, -1), (4, -2), (9, -3) contains points that lie on the graph of f(x)=xf(x) = -\sqrt{x}.

Would you like further details or have any questions?

Related Questions:

  1. How would the graph of f(x)=xf(x) = \sqrt{x} differ from f(x)=xf(x) = -\sqrt{x}?
  2. What is the domain and range of the function f(x)=xf(x) = -\sqrt{x}?
  3. How do you find the square root of a negative number in complex numbers?
  4. What transformations are applied to the function f(x)=xf(x) = \sqrt{x} to obtain f(x)=xf(x) = -\sqrt{x}?
  5. How would you plot f(x)=xf(x) = -\sqrt{x} using a graphing calculator?

Tip:

Remember, for square root functions like f(x)=xf(x) = \sqrt{x} or f(x)=xf(x) = -\sqrt{x}, the domain is restricted to non-negative values of xx.

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Math Problem Analysis

Mathematical Concepts

Square root function
Domain and range
Graphing functions

Formulas

f(x) = -√x

Theorems

Properties of square roots
Function transformations

Suitable Grade Level

Grades 9-12