Math Problem Statement

Find the value of f(6).

Solution

To solve for f(6)f(6), we need to determine the value of the function f(x)f(x) at x=6x = 6 using the graph provided.

Looking at the graph:

  • The function y=f(x)y = f(x) is a piecewise linear graph, with straight-line segments connecting different points on the coordinate plane.
  • From the graph, we observe that at x=6x = 6, the value of yy is 0 (since the graph touches the x-axis at this point).

Thus, f(6)=0f(6) = 0.

Would you like further details or explanations? Here are some follow-up questions that might help deepen your understanding:

  1. What is the general behavior of the graph for different intervals of xx?
  2. How can we determine the slope of the line segments in the graph?
  3. What does it mean when the graph intersects the x-axis?
  4. Can you describe how the function behaves as xx approaches negative or positive infinity?
  5. How would you find f(x)f(x) for any other specific value of xx?

Tip: When analyzing a graph, always pay attention to key points such as where the graph crosses the axes, and check for any changes in slope or direction.

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Math Problem Analysis

Mathematical Concepts

Function Evaluation
Graph Interpretation
Piecewise Linear Functions

Formulas

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Theorems

Graphical interpretation of functions

Suitable Grade Level

Grades 7-10