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The question asks: **Which of the following is NOT one-to-one?**

### Definitions:
- A **one-to-one function** (or injective function) is a function where every element of the range corresponds to exactly one element of the domain. In other words, no two different inputs can produce the same output.

Now, let's analyze each function:

1. \( k(x) = \sqrt{2x + 7} \)
   - The square root function is not one-to-one, because square roots produce both positive and negative values for the same input.
   - **Conclusion**: This function is **NOT one-to-one**.

2. \( k(x) = -\frac{5}{4} \)
   - This is a constant function. Constant functions are never one-to-one because all inputs give the same output.
   - **Conclusion**: This function is **NOT one-to-one**.

3. \( k(x) = \frac{4x}{5x - 6} \)
   - This is a rational function. To check if it is one-to-one, we would analyze its derivative or check for horizontal lines that intersect more than once. This function is likely one-to-one in most cases because rational functions typically don’t repeat values unless there's a specific symmetry.
   - **Conclusion**: This function is **likely one-to-one**.

4. \( k(x) = 3x \)
   - This is a linear function with a non-zero slope. Linear functions of this form are always one-to-one because every input maps to a unique output.
   - **Conclusion**: This function is **one-to-one**.

### Answer:
The **constant function** \( k(x) = -\frac{5}{4} \) is **NOT one-to-one**.

Would you like further clarification or details on one-to-one functions?

Here are 5 related questions to expand your understanding:
1. What is the definition of a bijective function?
2. How can we determine if a rational function is one-to-one?
3. What role does the derivative play in checking for injectivity?
4. Can a polynomial function be one-to-one? If so, which ones?
5. What are real-life examples of one-to-one functions?

**Tip**: To check if a function is one-to-one, you can use the **horizontal line test**—if any horizontal line intersects the graph of the function more than once, it is not one-to-one.

Which of the following is NOT one-to-one?
1. k(x) = sqrt(2x + 7)
2. k(x) = -5/4
3. k(x) = (4x) / (5x - 6)
4. k(x) = 3x

Analyze multiple functions to determine which one is NOT one-to-one. This problem covers key algebraic concepts like rational functions, linear functions, and injectivity, with applications of the horizontal line test. Suitable for students in Grades 9-12.

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