Which of the Following Graphs Represent a Function?
📝 Question
Determine which of the following graphs represents a function.
(a) and (b) are given graphs.
✅ Solution
🔹 Step 1: Use Vertical Line Test
A graph represents a function if every vertical line intersects the graph at most once.
🔹 Step 2: Analyze Graph (a)
In graph (a), any vertical line cuts the curve at only one point.
Thus, each value of \(x\) corresponds to exactly one value of \(y\).
Hence, graph (a) represents a function.
🔹 Step 3: Analyze Graph (b)
In graph (b), some vertical lines intersect the curve at more than one point.
This means a single value of \(x\) has multiple values of \(y\).
Hence, graph (b) does not represent a function.
🎯 Final Answer
\[ \boxed{\text{Graph (a) represents a function, while graph (b) does not}} \]
🚀 Exam Shortcut
- Draw imaginary vertical lines
- If line cuts once ⇒ Function
- If line cuts more than once ⇒ Not a function
- Remember: One input → only one output