Questions: Select the domain and range of the graph in set-builder and interval notation. Domain = x x ∈ R or (-∞, ∞) Range = y y ∈ R or (-∞, ∞)

Select the domain and range of the graph in set-builder and interval notation. Domain = x x ∈ R or (-∞, ∞) Range = y y ∈ R or (-∞, ∞)
Transcript text: Select the domain and range of the graph in set-builder and interval notation. Domain $=$ $\{x \mid x \in \mathbb{R}\}$ or $(-\infty, \infty)$ Range $=$ $\{ y \mid y \in \mathbb{R}\}$ or $(-\infty, \infty)$
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Solution

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Solution Steps

Step 1: Identify the Domain

The domain of a function is the set of all possible input values (x-values) that the function can accept. Observing the graph, the curve extends infinitely in both the positive and negative x-directions. Therefore, the domain includes all real numbers.

Step 2: Identify the Range

The range of a function is the set of all possible output values (y-values) that the function can produce. Observing the graph, the curve extends infinitely in both the positive and negative y-directions. Therefore, the range includes all real numbers.

Step 3: Express the Domain and Range in Set-Builder and Interval Notation
  • Domain in Set-Builder Notation: \(\{x \mid x \in \mathbb{R}\}\)
  • Domain in Interval Notation: \((-\infty, \infty)\)
  • Range in Set-Builder Notation: \(\{y \mid y \in \mathbb{R}\}\)
  • Range in Interval Notation: \((-\infty, \infty)\)

Final Answer

  • Domain: \(\{x \mid x \in \mathbb{R}\}\) or \((-\infty, \infty)\)
  • Range: \(\{y \mid y \in \mathbb{R}\}\) or \((-\infty, \infty)\)
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