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The question in the image asks the following:

**(b)** *What is a relation? What is a function? Given that \( g(m) = 32m^2d + 16/\sqrt{m} \), which symbol represents the independent variable? Dependent variable? Parameter?*

Let's break down and answer each part:

1. **What is a relation?**
   A **relation** in mathematics is a set of ordered pairs where the first element comes from a set of inputs and the second element comes from a set of outputs. Essentially, it's a rule that connects inputs to outputs, but it doesn’t necessarily have to be a function.

2. **What is a function?**
   A **function** is a specific type of relation where every input is associated with exactly one output. If a relation allows an input to be connected to more than one output, it’s not a function.

3. **Given that \( g(m) = 32m^2d + 16/\sqrt{m} \):**
   - **Independent variable**: The independent variable is the one that you can freely choose or control. In this case, \( m \) is the independent variable because the function \( g(m) \) depends on \( m \).
   - **Dependent variable**: The dependent variable is the result that changes depending on the independent variable. Here, \( g(m) \) is the dependent variable since it depends on \( m \).
   - **Parameter**: A parameter is a constant value that helps shape the form of the function but isn't the main variable that the function depends on. In this expression, \( d \) is likely a parameter because it modifies the form of the function but doesn’t vary like \( m \).

Would you like more details or further clarification on any part of this? Here are some related questions you might find interesting:

1. How can you tell if a relation is a function just by looking at its graph?
2. What are examples of relations that are not functions?
3. Can a function have more than one independent variable?
4. How does the parameter affect the shape or form of a function?
5. What are the similarities and differences between functions and equations?

**Tip:** In many cases, the independent variable is the one you directly control or input, while the dependent variable is the result you observe!

What is a relation? What is a function? Given that g(m) = 32m^2d + 16/√m, which symbol represents the independent variable? Dependent variable? Parameter?

Learn about functions and relations, and how to identify independent variables, dependent variables, and parameters in the expression g(m) = 32m^2d + 16/√m. This topic is suitable for high school students in Grades 9-12.

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