The images you provided present several graphs where the task is to determine if the function represented by the graph is one-to-one.

1. First Graph (first image):

   • This graph shows a curve that appears to have a horizontal tangent at some points, potentially leading to multiple x-values mapping to the same y-value (or vice versa). This suggests that the function is not one-to-one.
   • Answer: B. The function is not one-to-one.

2. Second Graph (first image):

   • This graph shows a line that is strictly increasing. For every distinct x-value, there is a unique corresponding y-value. This suggests the function is one-to-one.
   • Answer: A. The function is one-to-one.

3. Third Graph (first image):

   • This graph shows a straight line with a positive slope, which means that the function is increasing and hence one-to-one.
   • Answer: A. The function is one-to-one.

4. Fourth Graph (second image):

   • This graph shows a curve that goes upwards, then levels off, and then increases again. This curve likely fails the horizontal line test, meaning a horizontal line can intersect it at more than one point, indicating that the function is not one-to-one.
   • Answer: B. The function is not one-to-one.

5. Fifth Graph (second image):

   • This graph shows a straight line with a positive slope, indicating that the function is one-to-one.
   • Answer: A. The function is one-to-one.

If you need further explanations on the reasoning or any other clarification, feel free to ask!

Here are some related questions for deeper understanding:

1. What is the horizontal line test and how is it used to determine if a function is one-to-one?
2. How do you recognize whether a function is strictly increasing or decreasing just by looking at its graph?
3. What are some examples of functions that are one-to-one?
4. How does the concept of inverse functions relate to one-to-one functions?
5. Can a function be one-to-one if it has a horizontal tangent?

Tip: Always use the horizontal line test to check if a function is one-to-one: if any horizontal line intersects the graph more than once, the function is not one-to-one.