Math Problem Statement
Evaluate f(2) and solve f(x) = 2 based on the graph of the function f(x).
Solution
In the provided image, the function is graphed, and there are two tasks shown:
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Evaluate :
- From the graph, when , the function value . This part is correctly answered.
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Solve :
- To find where , look for the point(s) where the function intersects the line . From the graph, the function intersects the horizontal line at approximately . Therefore, the correct solution should be , not .
Would you like further explanation on this? Here are some related questions to deepen your understanding:
- What does it mean when a function intersects a specific line, like ?
- How can you verify solutions by substituting back into the function?
- What are the common methods to solve equations involving functions graphically?
- Can you describe what happens to the value of as increases for this graph?
- How do you find other key points on the graph, such as intercepts or turning points?
Tip: When solving equations graphically, always double-check the points of intersection visually or by using a ruler for more accuracy.
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Math Problem Analysis
Mathematical Concepts
Function Evaluation
Graphical Analysis
Formulas
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Theorems
Graphical Intersection Theorem
Suitable Grade Level
Grades 9-12