Math Problem Statement

The graph of a function f is shown below. Find one value of x for which f(x) = 4 and find f(-2).

Solution

Let's analyze the problem step by step.

Problem Breakdown:

  1. Question (a): Find one xx-value for which f(x)=4f(x) = 4.

    • Look for where the graph has a yy-coordinate of 44.
    • Locate the corresponding xx-coordinate.
  2. Question (b): Find f(2)f(-2).

    • Locate x=2x = -2 on the graph.
    • Find the yy-coordinate of the function at this xx-value.

Solution:

(a) Finding xx such that f(x)=4f(x) = 4:

From the graph:

  • f(x)=4f(x) = 4 occurs where the horizontal line y=4y = 4 intersects the function.
  • Looking at the graph, this happens at x=3x = -3.

Thus, one value of xx for which f(x)=4f(x) = 4 is: x=3x = -3

(b) Finding f(2)f(-2):

From the graph:

  • At x=2x = -2, the yy-coordinate is 33.

Thus: f(2)=3f(-2) = 3


Final Answers:

(a) x=3x = -3
(b) f(2)=3f(-2) = 3

Let me know if you need further clarification or want to go over details!


Additional Questions for Exploration:

  1. What is the slope of the line represented by the function f(x)f(x)?
  2. Can you determine the equation of the function f(x)f(x)?
  3. What happens to f(x)f(x) as xx \to \infty?
  4. Can you find xx such that f(x)=0f(x) = 0?
  5. What is f(0)f(0), and why?

Tip: Always identify key points (e.g., intercepts, specific values) to understand the behavior of a graph better.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Graph Interpretation

Formulas

None (graph reading)

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 6-8