Math Problem Statement

Evaluate f(1) and solve f(x) = 1 based on the given graph of the function f(x).

Solution

Let's analyze the graph and solve the questions based on it.

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

    • To find f(1)f(1), look for the value of f(x)f(x) when x=1x = 1. From the graph, at x=1x = 1, the function's value appears to be 4.
    • Therefore, f(1)=4f(1) = 4.
  2. Solve f(x)=1f(x) = 1:

    • To solve this, we need to find the xx-value where the function equals 1. From the graph, it seems that the function reaches f(x)=1f(x) = 1 when x=3x = 3.
    • Therefore, x=3x = 3.

Let me know if you'd like more details or have any questions!

Here are 5 related questions to deepen your understanding:

  1. What type of function might this be based on the shape of the curve?
  2. Can f(x)f(x) ever be negative based on the graph shown?
  3. How would you find f(2)f(2) using the graph?
  4. What is the general behavior of the function as xx increases?
  5. How would you graphically solve f(x)=2f(x) = 2?

Tip: When reading graphs, always carefully observe the points where the curve crosses grid lines to find function values accurately.

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Math Problem Analysis

Mathematical Concepts

Functions
Graph Interpretation

Formulas

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Theorems

Graph Reading

Suitable Grade Level

Grades 9-12