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In the given activity, you are asked to evaluate the function \( f(x) = 4x - 3 \) for specific values of \( x \) and determine its domain and range.

### Steps for solving the problem:

#### 1. **Evaluating the Function \( f(x) = 4x - 3 \)**:
You are provided with a set of \( x \) values: \( -15, -9, -3, 0, 2, 4, 6, 20 \). Let’s calculate the corresponding values of \( f(x) \) for each of these inputs:

\[
f(x) = 4x - 3
\]

- For \( x = -15 \):
  \[
  f(-15) = 4(-15) - 3 = -60 - 3 = -63
  \]
- For \( x = -9 \):
  \[
  f(-9) = 4(-9) - 3 = -36 - 3 = -39
  \]
- For \( x = -3 \):
  \[
  f(-3) = 4(-3) - 3 = -12 - 3 = -15
  \]
- For \( x = 0 \):
  \[
  f(0) = 4(0) - 3 = -3
  \]
- For \( x = 2 \):
  \[
  f(2) = 4(2) - 3 = 8 - 3 = 5
  \]
- For \( x = 4 \):
  \[
  f(4) = 4(4) - 3 = 16 - 3 = 13
  \]
- For \( x = 6 \):
  \[
  f(6) = 4(6) - 3 = 24 - 3 = 21
  \]
- For \( x = 20 \):
  \[
  f(20) = 4(20) - 3 = 80 - 3 = 77
  \]

#### 2. **Domain and Range**:
- **Domain**: The domain of the function is the set of all real numbers \( \mathbb{R} \) because there are no restrictions on \( x \) for the linear function \( f(x) = 4x - 3 \). The function can accept any real number.

  \[
  \text{Domain } f = \mathbb{R}
  \]

- **Range**: Since the function is linear and increases without bound as \( x \) increases, the range is also the set of all real numbers \( \mathbb{R} \).

  \[
  \text{Range } f = \mathbb{R}
  \]

#### 3. **Final Table**:

\[
\begin{array}{|c|c|}
\hline
x & f(x) = 4x - 3 \\
\hline
-15 & -63 \\
-9 & -39 \\
-3 & -15 \\
0 & -3 \\
2 & 5 \\
4 & 13 \\
6 & 21 \\
20 & 77 \\
\hline
\end{array}
\]

The graph next to the table suggests that the function is linear with a positive slope.

### Summary:
- **Domain**: \( \mathbb{R} \) (All real numbers)
- **Range**: \( \mathbb{R} \) (All real numbers)

Would you like more details or have any other questions?

Here are five related questions to expand on this topic:
1. How do you determine the slope and y-intercept from a linear function like \( f(x) = 4x - 3 \)?
2. What happens to the range if the function was quadratic instead of linear?
3. How can you use a graph to estimate the domain and range of a function?
4. What is the relationship between the slope of a line and how fast it grows or declines?
5. What is the effect on the graph of \( f(x) = 4x - 3 \) if we change the slope or intercept?

**Tip**: When evaluating functions for different values of \( x \), it's helpful to note patterns in how the output changes—this can give insights into the behavior of the function (e.g., linear growth in this case).

Determine the set of real numbers x for which the function f(x) = 4x - 3 can be evaluated and its domain and range. The function needs to be evaluated at specific points, and the domain and range of the function must be determined.

Explore how to evaluate the linear function f(x) = 4x - 3 at specific values of x, and learn how to determine the function's domain and range. The solution covers key algebraic concepts related to linear functions, suitable for students in Grades 9-12.

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