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:
-
Question (a): Find one -value for which .
- Look for where the graph has a -coordinate of .
- Locate the corresponding -coordinate.
-
Question (b): Find .
- Locate on the graph.
- Find the -coordinate of the function at this -value.
Solution:
(a) Finding such that :
From the graph:
- occurs where the horizontal line intersects the function.
- Looking at the graph, this happens at .
Thus, one value of for which is:
(b) Finding :
From the graph:
- At , the -coordinate is .
Thus:
Final Answers:
(a)
(b)
Let me know if you need further clarification or want to go over details!
Additional Questions for Exploration:
- What is the slope of the line represented by the function ?
- Can you determine the equation of the function ?
- What happens to as ?
- Can you find such that ?
- What is , 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