Math Problem Statement

Use the graph of f shown to find the indicated limit or function value. If the limit does not exist, explain why. What is the value of f(-3)?

Solution

To determine the value of f(3)f(-3) from the graph:

  1. Look at the point where x=3x = -3 on the graph.
  2. Identify the corresponding yy-value for this xx-value.

From the graph, when x=3x = -3, the point on the graph is (3,1)(-3, 1). This indicates that f(3)=1f(-3) = 1.

Thus, the correct answer is: 1\boxed{1}

Would you like further details or have any questions? Here are some related questions to consider:

  1. What is the value of f(2)f(2) based on the graph?
  2. Does the limit limx2f(x)\lim_{{x \to 2}} f(x) exist? If so, what is it?
  3. What is the value of f(3)f(3) according to the graph?
  4. What does it mean if the left-hand limit and right-hand limit at a point are not equal?
  5. How do you determine if a function is continuous at a certain point based on its graph?

Tip: When analyzing graphs, always check the exact points marked for any holes, jumps, or other discontinuities to accurately determine function values and limits.

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Math Problem Analysis

Mathematical Concepts

Functions
Graph Analysis
Limits

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12