Math Problem Statement
Solution
To determine if the given relation defines as a function of , we need to check whether every input value of has exactly one corresponding output value of .
The easiest way to verify this is by applying the vertical line test: if a vertical line drawn at any point along the graph intersects the graph in more than one place, then is not a function of .
Looking at the graph, no vertical line would intersect the graph at more than one point for any -value. Therefore, this relation does define as a function of .
Thus, the correct answer is:
- Yes, this relation defines as a function of .
Would you like more clarification or further questions?
Here are 5 follow-up questions:
- How does the vertical line test work in identifying functions?
- Can this function be represented by an equation?
- What would happen if a vertical line intersected the graph at two points?
- How can you use the horizontal line test to determine if a function is one-to-one?
- What type of function (e.g., polynomial, trigonometric) does this graph likely represent?
Tip: A function passes the vertical line test if each -value has only one -value!
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Math Problem Analysis
Mathematical Concepts
Functions
Graphing
Vertical Line Test
Formulas
-
Theorems
Vertical Line Test
Suitable Grade Level
Grades 9-12
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