https://file.aiquickdraw.com/mathbot/file/1726372835216zlu523ku.jpg

Let's analyze the function \( f(x) \) defined in the image and address each of the related questions.

### Function Definition:

\[
f(x) = 
\begin{cases} 
3x - 1 & \text{if } x \leq -2 \\
5 & \text{if } -2 < x \leq 4 \\
-2x + 5 & \text{if } x > 4 
\end{cases}
\]

### 20. **Determine el dominio de \( f \)**:
The domain of the function is the set of all \( x \)-values for which \( f(x) \) is defined. In this case, the function has different expressions for different intervals of \( x \), but it is defined for all real numbers. Hence, the domain is:

\[
D(f) = (-\infty, \infty)
\]

### 21. **¿Qué función se representa en el intervalo \( ] -\infty, -2] \)?**

In the interval \( x \leq -2 \), the function is defined by \( f(x) = 3x - 1 \). Therefore, the function represented in the interval \( ] -\infty, -2] \) is:

\[
f(x) = 3x - 1
\]

### 22. **¿Para los valores de \( x \in [-2, 4] \), la gráfica de la función es un punto?**

In

Sea la función f definida por: f(x) = {3x - 1; x <= -2, 5; -2 < x <= 4, -2x + 5; x > 4}. Determine el dominio de f, ¿Qué función se representa en el intervalo ] -∞, -2] ?, ¿Para los valores de x ∈ [-2, 4], la gráfica de la función es un punto? Grafique la función f.

Learn how to analyze a piecewise function defined by 3 different expressions, determine its domain, understand its representation in intervals, and explore its graphical behavior across intervals. Suitable for high school students in Grades 10-12.

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