To determine whether each graph represents a function, we use the
vertical line test. The vertical line test states that a graph represents a function if and only if every vertical line intersects the graph at most once. If any vertical line intersects the graph more than once, then the graph does not represent a function.
Let's analyze each graph step by step:
---
Graph 1:
- The graph is a parabola opening to the left.
- A vertical line can intersect this graph at
two points for certain values of \( x \).
-
Conclusion: This graph does
not represent a function.
---
Graph 2:
- The graph is a smooth curve that appears to be a sine wave or similar periodic function.
- No vertical line will intersect this graph more than once.
-
Conclusion: This graph
does represent a function.
---
Graph 3:
- The graph is a parabola opening upwards.
- No vertical line will intersect this graph more than once.
-
Conclusion: This graph
does represent a function.
---
Graph 4:
- The graph is a closed loop (a circle-like shape).
- A vertical line can intersect this graph at
two points for certain values of \( x \).
-
Conclusion: This graph does
not represent a function.
---
Graph 5:
- The graph is a straight line.
- No vertical line will intersect this graph more than once.
-
Conclusion: This graph
does represent a function.
---
Graph 6:
- The graph is a circle.
- A vertical line can intersect this graph at
two points for certain values of \( x \).
-
Conclusion: This graph does
not represent a function.
---
Graph 7:
- The graph is a hyperbola with two branches.
- No vertical line will intersect this graph more than once.
-
Conclusion: This graph
does represent a function.
---
Graph 8:
- The graph is a straight line.
- No vertical line will intersect this graph more than once.
-
Conclusion: This graph
does represent a function.
---
Graph 9:
- The graph is a parabola opening upwards.
- No vertical line will intersect this graph more than once.
-
Conclusion: This graph
does represent a function.
---
Final Answers:
1. Not a function
2. Function
3. Function
4. Not a function
5. Function
6. Not a function
7. Function
8. Function
9. Function
Boxed Answer:
\[
\boxed{
\text{1) No, 2) Yes, 3) Yes, 4) No, 5) Yes, 6) No, 7) Yes, 8) Yes, 9) Yes}
}
\]
Parent Tip: Review the logic above to help your child master the concept of functions and graphs worksheet.
