Question

suppose that you are holding your toy submarine under the water. you release it and it begins to ascend. the graph models the depth of the submarine as a function of time. what is the domain and range of the function in the graph? graph of a line from (0, -7) to (3, -1) d: \square \leq t \leq \square r: \square \leq d \leq \square

Explanation:

Step1: Determine the domain

The domain of a function is the set of all possible input values (time \( t \) in this case). From the graph, the time starts at \( t = 0 \) (when the submarine is released) and ends at \( t = 3 \) (when it reaches the surface, depth \( d = 0 \)). So the domain is \( 0 \leq t \leq 3 \).

Step2: Determine the range

The range of a function is the set of all possible output values (depth \( d \) in this case). The depth starts at \( d=-7 \) (when \( t = 0 \)) and goes up to \( d = 0 \) (when \( t = 3 \)). So the range is \( -7 \leq d \leq 0 \).

Answer:

Domain: \( \boldsymbol{0 \leq t \leq 3} \) (so fill 0 and 3 in the domain boxes)
Range: \( \boldsymbol{-7 \leq d \leq 0} \) (so fill -7 and 0 in the range boxes)