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Determine whether the value of x is given or the value of​ f(x) is given. Remember that x represents the number of years since 1900. Remember to type an integer or a decimal.

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To solve the problem, we need to determine whether the value provided is for \( x \) (the number of years since 1900) or for \( f(x) \) (a function that depends on \( x \)).

Let's break it down based on the two possibilities:

1. **If you are given the number of years**:
   - The value is \( x \), where \( x \) represents the number of years since 1900. This is the input to the function \( f(x) \).
   - For example, if you are given the year 1950, then \( x = 1950 - 1900 = 50 \).

2. **If you are given the value of \( f(x) \)**:
   - The value is the output of the function \( f(x) \), which depends on the input \( x \). In this case, \( f(x) \) would be a result of the function based on the number of years since 1900.

To proceed, look at the information provided:

- If the value represents a number of years since 1900 (like 40 or 60), it’s an \( x \)-value.
- If the value represents a measurement or outcome (like population, temperature, or another calculated quantity), it’s \( f(x) \).

### Example 1: 
If you are told "the population in 1940 was 150,000," the year 1940 corresponds to \( x = 40 \), and 150,000 is \( f(40) \).

### Example 2:
If you are told "find the population in 1920," then \( x = 1920 - 1900 = 20 \), and you are looking for \( f(20) \).

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Would you like to clarify any part or explore more details?

### Additional Questions:
1. How would you determine \( x \) if you are given a year in the 21st century?
2. What kind of situations could \( f(x) \) represent in real-life problems?
3. How would you interpret the function \( f(x) \) if given a population growth model?
4. What does \( f(x) = 0 \) imply in terms of years since 1900?
5. If given a quadratic equation for \( f(x) \), how would you find the maximum population?

#### Tip:
Always subtract 1900 from any given year to find the corresponding \( x \)-value.

Determine whether the value of x is given or the value of f(x) is given. Remember that x represents the number of years since 1900. Remember to type an integer or a decimal.

Understand how to determine whether the value of x (years since 1900) or f(x) (a dependent variable) is given. This guide includes key concepts in functions and linear equations, suitable for students in Grades 6-8.

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