Math Problem Statement

The plot represents the function f(x). Evaluate f(2) and solve f(x) = 2.

Solution

Let's analyze the graph and the questions:

  1. Evaluate f(2)f(2):

    • Looking at the graph, when x=2x = 2, the function value f(x)f(x) corresponds to a yy-value of approximately 4.
    • So, f(2)=4f(2) = 4.
  2. Solve f(x)=2f(x) = 2:

    • To solve f(x)=2f(x) = 2, we look for the xx-value where the function reaches a yy-value of 2.
    • From the graph, this occurs at x=0x = 0.
    • Therefore, x=0x = 0 when f(x)=2f(x) = 2.

Summary:

  • f(2)=4f(2) = 4
  • f(x)=2f(x) = 2 at x=0x = 0

Would you like further details or clarification on this?

Here are five related questions:

  1. What is f(1)f(1) based on the graph?
  2. What happens to f(x)f(x) as xx increases beyond 5?
  3. Is the function f(x)f(x) increasing or decreasing for negative xx?
  4. Can you estimate f(1)f(-1) using the graph?
  5. How would you describe the general shape of the function?

Tip: When solving graph-based problems, always check key points and trends in the graph for accuracy.

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Math Problem Analysis

Mathematical Concepts

Function Evaluation
Graph Interpretation
Linear Functions

Formulas

f(x) represents the y-value for a given x

Theorems

Graphical interpretation of functions

Suitable Grade Level

Grades 6-8