Math Problem Statement

Evaluate f(-3) where f(x) is the piecewise function graphed.

Solution

To find f(3)f(-3) from the graph of the piecewise function, let's analyze the graph at the point where x=3x = -3.

From the graph:

  1. At x=3x = -3, the function's value corresponds to the filled blue dot at the point (3,3)(-3, -3).
  2. The filled dot indicates that the function is defined at this point, and the value of the function is the yy-coordinate of the point, which is 3-3.

Thus, f(3)=3f(-3) = -3.

Would you like a detailed explanation of how piecewise functions work or have any other questions?

Here are some follow-up questions:

  1. What is a piecewise function, and how is it defined?
  2. How can you tell if a function is defined at a specific point on a graph?
  3. How do you handle open and closed points on a graph?
  4. What are the key properties of continuous functions in piecewise graphs?
  5. How do you evaluate a piecewise function from a given equation instead of a graph?

Tip: In piecewise functions, a filled dot means the function is defined at that point, while an open circle means it's not.

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Graphing Functions

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9