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The image contains a set of mathematical equations, and the task is to express them in the form of inequalities. Here's the transcription of the text and the equations:

**1. Expresar gráficamente en \( \mathbb{R} \) las siguientes ecuaciones e inecuaciones. Se sugiere complementar la resolución de este ejercicio con GeoGebra.**

(a) \( y = -1 \)

(b) \( x = 2 \)

(c) \( 0.5 < x \leq 4 \)

(d) \( x^2 - 2x + 1 = 0 \)

(e) \( x^2 + y^2 = 4 \)

(f) \( y^2 = 4x \)

(g) \( y = x^2 + 3 \)

### Explanation:
To graphically express these equations and inequalities in \( \mathbb{R} \), here are the interpretations:

1. **(a) \( y = -1 \):**  
   This represents a horizontal line at \( y = -1 \).

2. **(b) \( x = 2 \):**  
   This represents a vertical line at \( x = 2 \).

3. **(c) \( 0.5 < x \leq 4 \):**  
   This is a vertical strip between \( x = 0.5 \) and \( x = 4 \), with the boundary at \( x = 0.5 \) not included and the boundary at \( x = 4 \) included.

4. **(d) \( x^2 - 2x + 1 = 0 \):**  
   This can be factored as \( (x-1)^2 = 0 \), meaning \( x = 1 \). Graphically, this is a vertical line at \( x = 1 \).

5. **(e) \( x^2 + y^2 = 4 \):**  
   This represents a circle centered at the origin \( (0,0) \) with radius 2.

6. **(f) \( y^2 = 4x \):**  
   This is a parabola that opens to the right with its vertex at \( (0,0) \).

7. **(g) \( y = x^2 + 3 \):**  
   This is a parabola opening upwards with its vertex at \( (0,3) \).

Would you like further details on any of these concepts or the graphical representation? 

Here are 5 related questions for further exploration:

1. How would the graph of \( y = -x + 2 \) compare to that of \( y = x + 2 \)?
2. How can you determine the intersection points between two parabolas?
3. What changes occur to the graph of a circle if the equation changes from \( x^2 + y^2 = 4 \) to \( x^2 + y^2 = 9 \)?
4. How does the inequality \( x^2 - 2x + 1 \leq 0 \) differ graphically from the equation \( x^2 - 2x + 1 = 0 \)?
5. How do the graph and solution set of \( y^2 = 4x \) change if the equation is modified to \( y^2 = 4x + 1 \)?

**Tip:** Use graphing tools like GeoGebra to visualize these equations and inequalities, as they provide an intuitive understanding of how changes in equations affect their graphs.

Explore how to graph equations and inequalities including circles, parabolas, and linear equations. Learn about key formulas for quadratic equations, circle equations, and parabola equations, with detailed examples and explanations suitable for high school students.

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