Math Problem Statement

Given the graph of y = f(x), what is the value of f(4)?

Solution

The image shows a graph of a piecewise function f(x)f(x), with a prompt asking for the value of f(4)f(4).

From the graph:

  1. Locate x=4x = 4 on the x-axis.
  2. Find the corresponding point on the graph.
  3. The y-coordinate of this point is the value of f(4)f(4).

Based on the graph, the point corresponding to x=4x = 4 is (4,4)(4, -4). Therefore, f(4)=4f(4) = -4.

Would you like any further details on this, or do you have any other questions?

Here are some related questions for further exploration:

  1. What is the value of f(2)f(-2) based on the graph?
  2. Can you describe the general behavior of the function f(x)f(x) as xx increases?
  3. What is the value of f(x)f(x) when x=2x = 2?
  4. What is the domain and range of the given function?
  5. How does the function f(x)f(x) behave at the points where it changes direction?

Tip: When reading a graph, always carefully identify the scale of both the x-axis and y-axis to ensure accurate interpretation of points.

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Graph Reading

Formulas

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Theorems

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Suitable Grade Level

Grades 9-11