Question

a penguin is swimming 300 meters below sea level before beginning to swim to the surface at a constant speed. the graph shows the penguin’s distance in meters from the surface after beginning its ascension for x minutes. penguin’s surfacing graph of a line from (0, -300) to (4, 0) with x-axis labeled time (min) and y-axis labeled depth (meters) 10. what are the domain and range of the function for this situation? choose two correct answers. - domain: all real numbers greater than or equal to -300 and less than or equal to 0 - domain: all real numbers greater than or equal to -300 and less than or equal to 4 - domain: all real numbers greater than or equal to 0 and less than or equal to 4 - range: all real numbers greater than or equal to -300 and less than or equal to 0 - range: all real numbers greater than or equal to -300 and less than or equal to 4 - range: all real numbers greater than or equal to 0 and less than or equal to 4

Explanation:

Step1: Analyze Domain

The domain represents the time \( x \) (in minutes) the penguin ascends. From the graph, \( x \) starts at 0 (beginning of ascension) and ends at 4 (when it reaches the surface). So domain is \( 0 \leq x \leq 4 \), i.e., all real numbers \( \geq 0 \) and \( \leq 4 \).

Step2: Analyze Range

The range represents the depth \( y \) (in meters). The penguin starts at -300 meters (300m below surface) and ascends to 0 meters (surface). So range is \( -300 \leq y \leq 0 \), i.e., all real numbers \( \geq -300 \) and \( \leq 0 \).

Answer:

Domain: All real numbers greater than or equal to 0 and less than or equal to 4
Range: All real numbers greater than or equal to -300 and less than or equal to 0