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The image contains an activity that requires determining the domain and range of the polynomial function \( f(x) = 4x - 3 \). Let's walk through the different parts of the problem:

### Function Information:
The function given is \( f(x) = 4x - 3 \), which is a linear function.

#### Domain (Dom f):
The domain of a linear function is all real numbers because there are no restrictions (like division by zero or square roots of negative numbers) that would limit the values of \(x\). Therefore, the domain is:
\[
Dom \, f = (-\infty, \infty)
\]

#### Range (Rango f):
Since the function is linear and its slope is non-zero (\(4\)), the range will also cover all real numbers. A linear function can take any real value as \(x\) varies over all real numbers. So, the range is:
\[
Rango \, f = (-\infty, \infty)
\]

### Table of Values:
There is a table in the image where you need to evaluate \( f(x) = 4x - 3 \) at specific values of \(x\):

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

### Question: 
"¿Hay alguno o más números reales para los cuales no se puedan realizar las operaciones \(4(x) - 3\)?"

No, there are no real numbers for which the operations cannot be performed, because the function is linear and defined for all real \(x\).

Would you like further details or clarifications? Here are 5 related questions to expand on this topic:

1. What would the domain and range be for a quadratic function instead of a linear one?
2. How do we determine if a function is one-to-one, and is this function one-to-one?
3. How does the slope of the linear function \(f(x) = 4x - 3\) affect the graph of the function?
4. Can you explore the behavior of the function \(f(x)\) as \(x\) approaches positive and negative infinity?
5. How would the function \(f(x) = 4x - 3\) change if the slope or the constant term was modified?

**Tip:** Always pay attention to the slope of a linear function, as it directly influences the steepness and direction of the line.

Determina el conjunto de números reales x, para los cuales es posible evaluar la función numérica f(x) = 4x - 3.

Explore how to determine the domain and range of the linear function f(x) = 4x - 3. The domain includes all real numbers, and the range is also all real numbers. This problem involves evaluating f(x) at specific points such as -15, -9, 0, 2, 4, 6, and 20.

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