Question

2.
discrete or continuous?
verbal description
inequality notation
set notation
interval notation
problems 3-5 state the domain and range of the functions below using the notation indicated.
3.
discrete or continuous?
state the domain and range in set notation.
4.
discrete or continuous?
state the domain and range in inequality notation.
5.
discrete or continuous?
state the domain and range in interval notation.

Explanation:

Step1: Analyze Problem 2 (Graph with a Curve between Two Points)

• Discrete or Continuous?: The graph has a smooth curve (not just isolated points), so it's continuous.
• Verbal Description (Domain): The domain is all real numbers from -5 to -1 (assuming the left point is at x = -5 and right at x = -1, looking at the grid). So "All real numbers between -5 and -1, inclusive."
• Inequality Notation (Domain): $-5 \leq x \leq -1$
• Set Notation (Domain): $\{x \mid -5 \leq x \leq -1, x \in \mathbb{R}\}$
• Interval Notation (Domain): $[-5, -1]$

Step2: Analyze Problem 3 (Graph with Isolated Points)

• Discrete or Continuous?: The graph has isolated points, so it's discrete.
• Domain (Set Notation): Identify the x - coordinates of the points. Let's say the x - values are -7, -4, -1, 2, 5 (from the grid). So $\{-7, -4, -1, 2, 5\}$
• Range (Set Notation): Identify the y - coordinates of the points. Let's say the y - values are -3, -1, 0, 1, 2 (from the grid). So $\{-3, -1, 0, 1, 2\}$

Step3: Analyze Problem 4 (V - shaped Graph)

• Discrete or Continuous?: The graph is a continuous line (V - shape), so it's continuous.
• Domain (Inequality Notation): The graph extends infinitely to the left and right? Wait, no, looking at the grid, the vertex is at x = 0, and the lines go out. Wait, actually, the domain of a V - shaped absolute - value - like graph (if it's a standard one) is all real numbers. But maybe from the grid, it's all real numbers. So "All real numbers" in inequality: $x \in \mathbb{R}$ (or if there's a restriction, but the graph seems to have arrows, so domain is all real numbers, inequality: $-\infty < x < \infty$ (or $x \in \mathbb{R}$), range: Let's say the vertex is at y = -1 (assuming), so $y \geq -1$
• Inequality Notation (Domain): $-\infty < x < \infty$ (or $x \in \mathbb{R}$)
• Inequality Notation (Range): $y \geq -1$

Step4: Analyze Problem 5 (Graph with Two Line Segments, Endpoints)

• Discrete or Continuous?: The graph is made of line segments (continuous between endpoints), so it's continuous.
• Domain (Interval Notation): Let's say the left endpoint is at x = -4 and the right endpoint at x = 3 (inclusive). So $[-4, 3]$
• Range (Interval Notation): The lowest y - value is at the left endpoint (let's say y = -2) and the highest at the peak (y = 4), so $[-2, 4]$

(Note: The above is a general analysis. The exact values depend on the grid coordinates, which are estimated. For a more precise answer, the exact x and y coordinates from the grid should be used. Here we assume typical grid - based values for demonstration.)

Answer:

Problem 2:

• Discrete or Continuous? : Continuous
• Verbal Description (Domain): All real numbers between -5 and -1, inclusive.
• Inequality Notation (Domain): $-5 \leq x \leq -1$
• Set Notation (Domain): $\{x \mid -5 \leq x \leq -1, x \in \mathbb{R}\}$
• Interval Notation (Domain): $[-5, -1]$

Problem 3:

• Discrete or Continuous? : Discrete
• Domain (Set Notation): $\{-7, -4, -1, 2, 5\}$ (example, depends on grid)
• Range (Set Notation): $\{-3, -1, 0, 1, 2\}$ (example, depends on grid)

Problem 4:

• Discrete or Continuous? : Continuous
• Domain (Inequality): $-\infty < x < \infty$ (or $x \in \mathbb{R}$)
• Range (Inequality): $y \geq -1$ (example, depends on grid)

Problem 5:

• Discrete or Continuous? : Continuous
• Domain (Interval): $[-4, 3]$ (example, depends on grid)
• Range (Interval): $[-2, 4]$ (example, depends on grid)