To determine which graph represents a function, we use the
Vertical Line Test.
Step 1: Understand the Vertical Line Test
The rule is simple: A graph represents a function if and only if no vertical line intersects the graph at more than one point.
- If you can draw a vertical line that hits the curve in two or more places, it is
not a function.
- If every possible vertical line hits the curve at most once (or not at all), it
is a function.
Step 2: Analyze Graph A
Look at the wavy line labeled "A". Imagine drawing a vertical line through the middle of the wave (for example, where $x = 0$).
- This vertical line would cross the top part of the wave.
- It would also cross the bottom part of the wave.
- Since the vertical line touches the graph in more than one place, Graph A fails the test. Therefore, A is not a function.
Step 3: Analyze Graph B
Look at the curve labeled "B". Imagine drawing vertical lines anywhere along this graph from left to right.
- No matter where you draw a vertical line, it will only touch the blue curve at exactly one point.
- There are no loops or overlapping sections where a single $x$-value has multiple $y$-values.
- Since no vertical line intersects the graph more than once, Graph B passes the test. Therefore, B is a function.
Conclusion
Graph A is not a function because it fails the vertical line test. Graph B is a function because it passes the vertical line test. The correct option corresponds to "Only B".
Final Answer:
2) B
Parent Tip: Review the logic above to help your child master the concept of functions vertical line test worksheet.
