Question

what are the domain and range of the function on the graph?

• the domain includes all integers, and the range is \\(y \ge 0\\).
• the domain includes all integers, and the range is \\(y > 0\\).
• the domain includes all real numbers, and the range is \\(y \ge 0\\).
• the domain includes all real numbers, and the range is \\(y > 0\\).

Explanation:

Analyze the domain of the graphed function

$$ \text{Domain} = (-\infty, \infty) = \mathbb{R} $$

Analyze the range of the graphed function

$$ \text{Range} = (0, \infty) \implies y > 0 $$

Match with the given options

$$ \text{Domain: all real numbers, Range: } y > 0 $$

Answer:

• The domain includes all integers, and the range is \(y \ge 0\).
• The domain includes all integers, and the range is \(y > 0\).
• The domain includes all real numbers, and the range is \(y \ge 0\).
• The domain includes all real numbers, and the range is \(y > 0\). (Correct answer)