To determine which of the graphs represent one-to-one functions, we can apply the horizontal line test. A function is one-to-one if and only if every horizontal line crosses the graph at most once.

Now, let’s go through each graph:

1. Graph a (Top graph): This graph appears to be a sinusoidal wave. A horizontal line can intersect this curve at multiple points, so it is not a one-to-one function.

2. Graph b (Second graph): The curve represents a vertical ellipse. A horizontal line can intersect this ellipse twice, so it is not a one-to-one function.

3. Graph c (Third graph): This is a straight line with a positive slope. A horizontal line will intersect it only once at most, meaning it is a one-to-one function.

4. Graph d (Fourth graph): This is a V-shaped function, likely an absolute value function. A horizontal line can intersect the two arms of the "V" at two points, so it is not a one-to-one function.

5. Graph e (Fifth graph): This is a parabolic curve opening upwards. A horizontal line will intersect this curve twice, so it is not a one-to-one function.

Thus, only Graph c represents a one-to-one function.

Would you like further details or have any questions on this?

Here are five related questions for you to explore:

1. How does the horizontal line test differ from the vertical line test?
2. Why is it important for a function to be one-to-one when determining its inverse?
3. Can a quadratic function ever be a one-to-one function?
4. How do transformations (e.g., shifts or stretches) affect the one-to-one nature of a graph?
5. What is the mathematical definition of an injective (one-to-one) function?

Tip: A function is considered one-to-one (injective) if different inputs always produce different outputs.