To determine if a graph represents a one-to-one function, we use the Horizontal Line Test. A function is one-to-one if no horizontal line intersects the graph more than once.

Let's analyze each graph from the images you provided:

Graph 1:

• The points are scattered, and there are vertical sections with multiple points aligned vertically. This suggests a No, this is not one-to-one.

Graph 2:

• This graph appears to be a sinusoidal curve, and horizontal lines will intersect the graph at multiple points, indicating the function is not one-to-one.

Graph 3:

• The function seems to have distinct outputs for distinct inputs, meaning each input gives a unique output. Therefore, it is one-to-one.

Graph 4:

• This graph is a decreasing curve, and for any horizontal line, it intersects the curve at most once. So, this graph is one-to-one.

Graph 5:

• This is a linear function. A straight line always passes the horizontal line test, so it is one-to-one.

Graph 6:

• This graph shows a parabola, which fails the horizontal line test because horizontal lines intersect it at two points. So, this graph is not one-to-one.

Summary:

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

Would you like to explore any of these graphs in more detail or need further clarification? Here are some related questions:

1. What is the Horizontal Line Test, and how does it apply to other functions?
2. How can we determine if a quadratic function is one-to-one?
3. What characteristics make a function one-to-one besides the Horizontal Line Test?
4. Can an exponential function ever fail the Horizontal Line Test?
5. How do rational functions behave with the Horizontal Line Test?

Tip: Remember, for functions like polynomials (except linear ones) or trigonometric functions, horizontal lines often intersect them at multiple points, meaning they aren't typically one-to-one.