Math Problem Statement

Evaluate f(3) and solve f(x) = 3 based on the graph of the function f(x).

Solution

Let's analyze the graph of the function f(x)f(x) from the image you uploaded.

1. Evaluate f(3)f(3):

To evaluate f(3)f(3), we find the value of the function when x=3x = 3. From the graph, locate the point where x=3x = 3. By following the vertical line upwards, we see that the function value at x=3x = 3 corresponds to f(3)=4f(3) = 4.

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

2. Solve f(x)=3f(x) = 3:

To solve f(x)=3f(x) = 3, we look for the xx-value where the function's output is 3. By finding the horizontal line at f(x)=3f(x) = 3 on the graph, it intersects the curve at around x2x \approx 2.

Therefore, the solution is approximately: x2.x \approx 2.

Would you like further details on these calculations, or any additional questions?

Here are some relative questions to explore further:

  1. How can you use the graph to estimate other values of f(x)f(x)?
  2. What are the key features of the function in the graph, such as intercepts and asymptotes?
  3. Can we determine the behavior of f(x)f(x) as xx approaches positive and negative infinity?
  4. What type of function does the graph likely represent (e.g., exponential, quadratic)?
  5. How would the solution change if f(x)=5f(x) = 5 instead of f(x)=3f(x) = 3?

Tip: When interpreting graphs, always carefully check the scales on both the x- and y-axes for accurate evaluation of values!

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Math Problem Analysis

Mathematical Concepts

Functions
Graph Interpretation

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8