Math Problem Statement

Based on the query submitted by the user and the corresponding solution, generate the following information in JSON format.

Solution

Let's analyze the graph in the image to solve for f(4)f(4).

The graph shows a straight line, so the function f(x)f(x) is linear. To find f(4)f(4), follow these steps:

  1. Locate x=4x = 4 on the x-axis.
  2. From x=4x = 4, move vertically to meet the graph of the function.
  3. Determine the corresponding yy-coordinate at this point on the graph.

Step-by-Step Analysis

  • On the x-axis, at x=4x = 4, the graph intersects at y=3y = -3.

Thus, f(4)=3f(4) = -3.

Final Answer:

f(4)=3f(4) = -3

Would you like a detailed explanation of how to verify this or explore more about linear functions?

Here are 5 related questions you might find helpful:

  1. How can we find the equation of a straight line given a graph?
  2. What is the slope of the function in this graph?
  3. How do you compute f(x)f(x) for other values of xx using the equation of the line?
  4. Can we determine where f(x)=0f(x) = 0 on this graph?
  5. How does changing the slope affect the graph of a linear function?

Tip: When reading values from a graph, ensure you interpret the scales on both axes carefully to avoid mistakes!

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Graphing
Function Evaluation

Formulas

f(x) = mx + b (general form of a linear function)

Theorems

Graph of a Linear Function
Function Evaluation from a Graph

Suitable Grade Level

Grades 7-9