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The image you've uploaded discusses the evaluation of functions, specifically showing how to substitute a value for \(x\) in a function.

### Concept Notes:
- **Evaluating a function** involves replacing the variable in the function with a specific value and computing the result.
- For example, the given function is \( f(x) = 2x + 1 \). If you need to evaluate it at \( x = 3 \), you substitute 3 into the function:
  \[
  f(3) = 2(3) + 1 = 6 + 1 = 7
  \]

### Example:
- Function: \( f(x) = 2x + 1 \)
- Evaluate for \( x = 3 \):

Solution steps:
1. \( f(3) = 2(3) + 1 \)
2. \( f(3) = 6 + 1 \)
3. \( f(3) = 7 \)

### Exercises:
The two given exercises are:
1. Evaluate \( f(x) = 2x \) at \( x = 3 \)
2. Evaluate \( f(x) = 2x - 7 \) at \( x = 4 \)

Would you like to solve these exercises with detailed steps?

Here are 5 related questions to expand your understanding:
1. What happens to the function's output if we increase the value of \( x \) in \( f(x) = 2x + 1 \)?
2. How would you evaluate the function \( f(x) = 3x^2 + 4x - 5 \) at \( x = 2 \)?
3. What is the meaning of the domain of a function when evaluating it?
4. How would the function change if you replaced \( 2x \) with \( x^2 \) in \( f(x) = 2x + 1 \)?
5. Can a function be evaluated for a non-numerical input? If so, what type of function would allow that?

**Tip**: Always substitute values carefully and simplify the expression step by step to avoid mistakes.

Evaluate the function f(x) = 2x + 1 at x = 3. Then, solve the exercises: 1) f(x) = 2x at x = 3 and 2) f(x) = 2x - 7 at x = 4.

Learn how to evaluate the function f(x) = 2x + 1 at x = 3 with detailed steps, and practice additional exercises on evaluating functions for different inputs. Suitable for Grades 6-8 students learning function evaluation in algebra.

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