To determine whether each graph represents a one-to-one function, we can use the horizontal line test. A function is one-to-one if each horizontal line crosses the graph at most once. Here’s the analysis:

1. Graph 1:

   • This is a parabolic graph that opens upwards.
   • A horizontal line would intersect this curve more than once.
   • Answer: No (not one-to-one).

2. Graph 2:

   • This graph appears to be a line with a constant negative slope.
   • A horizontal line will only intersect this line at one point.
   • Answer: Yes (one-to-one).

3. Graph 3:

   • This graph is a wavy curve, likely sinusoidal.
   • A horizontal line would intersect it multiple times.
   • Answer: No (not one-to-one).

4. Graph 4:

   • This graph consists of individual points (not a continuous function).
   • Some y-values are repeated (e.g., two points have y = 2).
   • Answer: No (not one-to-one).

5. Graph 5:

   • Similar to Graph 4, it’s a collection of discrete points.
   • There are repeated y-values, so it’s not one-to-one.
   • Answer: No (not one-to-one).

6. Graph 6:

   • This is a line with a negative slope, representing a linear function.
   • A horizontal line would intersect this line at only one point.
   • Answer: Yes (one-to-one).

Summary:

• Graph 1: No
• Graph 2: Yes
• Graph 3: No
• Graph 4: No
• Graph 5: No
• Graph 6: Yes

Would you like a deeper explanation of one-to-one functions?

1. What is the horizontal line test, and how is it used in this context?
2. Can parabolas ever represent one-to-one functions?
3. Why do discrete graphs like Graph 4 and Graph 5 often fail to be one-to-one?
4. What are some characteristics of functions that are always one-to-one?
5. How does the slope of a line relate to its status as a one-to-one function?

Tip: Remember, if a function is strictly increasing or decreasing over its domain, it is one-to-one by definition!