Math Problem Statement

Select the points that are NOT roots (zeroes) of f(x) based on the graph.

Solution

The problem asks to select the points that are NOT roots (zeroes) of the function f(x)f(x). The roots (zeroes) are the x-values where the graph crosses or touches the x-axis, meaning where f(x)=0f(x) = 0.

Let’s go through the graph and identify the roots:

  • At x=2.8x = -2.8: The graph crosses the x-axis, so this is a root.
  • At x=1.2x = -1.2: The graph crosses the x-axis again, so this is also a root.
  • At x=1x = -1: The graph does not cross the x-axis, but there is an open circle at x=1x = -1 indicating that the function does not equal zero at this point. Thus, this is not a root.
  • At x=0x = 0: The graph does not touch or cross the x-axis here. Therefore, x=0x = 0 is not a root.
  • At x=1.5x = 1.5: The graph crosses the x-axis, so this is a root.
  • At x=2x = 2: There is a closed circle on the x-axis, meaning the function equals zero here. Thus, this is a root.
  • At x=3.75x = 3.75: The graph does not touch or cross the x-axis here. Therefore, x=3.75x = 3.75 is not a root.
  • At x=4x = 4: The graph is above the x-axis and does not cross or touch it, so x=4x = 4 is not a root.

The points that are NOT roots of f(x)f(x) are:

  • x=1x = -1
  • x=0x = 0
  • x=3.75x = 3.75
  • x=4x = 4

Would you like further details or explanations on any specific part of this process?

Here are some related questions:

  1. What is the mathematical definition of a root (zero) of a function?
  2. How do open circles affect the interpretation of function values?
  3. What is the significance of closed circles on graphs?
  4. How would you find the roots of a function analytically?
  5. How do turning points relate to roots?

Tip: A root of a function occurs at points where the function's graph intersects the x-axis or touches it with a closed circle, indicating f(x)=0f(x) = 0 at those points.

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Math Problem Analysis

Mathematical Concepts

Roots of a function
Zeroes of a function
Graph interpretation

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12