Questions: Determine the domain and range. Domain: x -2 ≤ x ≤ 2; range: y -4 ≤ y ≤ 4 Domain: all real numbers; range: all real numbers Domain: x x ≥ 2; range: y y ≥ 4 Domain: x -4 ≤ x ≤ 4; range: y -2 ≤ y ≤ 2

Determine the domain and range. Domain: x -2 ≤ x ≤ 2; range: y -4 ≤ y ≤ 4 Domain: all real numbers; range: all real numbers Domain: x x ≥ 2; range: y y ≥ 4 Domain: x -4 ≤ x ≤ 4; range: y -2 ≤ y ≤ 2
Transcript text: Determine the domain and range. Domain: $\{x \mid-2 \leq x \leq 2\}$; range: $\{y \mid-4 \leq y \leq 4\}$ Domain: all real numbers; range: all real numbers Domain: $\{x \mid x \geq 2\}$; range: $\{y \mid y \geq 4\}$ Domain: $\{x \mid-4 \leq x \leq 4\}$; range: $\{y \mid-2 \leq y \leq 2\}$
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Solution

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Solution Steps

Step 1: Identify the shape and its properties

The graph shows a circle centered at the origin (0,0) with a radius of 4 units.

Step 2: Determine the domain

The domain of a circle is the set of all possible x-values. Since the circle extends from -4 to 4 on the x-axis, the domain is \([-4, 4]\).

Step 3: Determine the range

The range of a circle is the set of all possible y-values. Since the circle extends from -4 to 4 on the y-axis, the range is \([-4, 4]\).

Final Answer

  • Domain: \([-4 \leq x \leq 4]\)
  • Range: \([-4 \leq y \leq 4]\)

The correct option is:

  • Domain: \([-4 \leq x \leq 4]\); range: \([-4 \leq y \leq 4]\)
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