Question

problems 6–7: aba described yesterday morning at school like this: i entered the school on the ground floor, then walked up the stairs to the third floor to attend an hour - long class. afterward, i had an hour - long class in the basement, then i went up to the ground floor and sat outside to eat my lunch. 6. label both axes. 7. sketch a possible graph of aba’s height from the ground floor as a function of time. problems 8–9: here is a graph of speed and time. 8. which sport could this graph represent? a. fishing b. skydiving c. 100 - yard sprint d. golf e. soccer 9. describe how you think that sport fits the graph. spiral review 10. the function ( p(t) ) represents the height of water in a bathtub, in inches, after ( t ) minutes. match each sentence to its equation. a. after 20 minutes, the bathtub is empty. ( p(10)=4 ) b. the bathtub starts out with no water. ( p(t)=w ) c. after 10 minutes, the height of the water is 4 inches. ( p(20)=0 ) d. the height of the water is 10 inches after 4 minutes. ( p(0)=0 ) e. the height of the water is ( w ) inches after ( t ) minutes. ( p(4)=10 ) reflection 1. put a question mark next to a problem you’re feeling unsure of. 2. use this space to ask a question or share something you’re proud of.

Explanation:

Problem 6

To label the axes for Aba's height - time graph, the x - axis should represent time (in hours or minutes, as the events are hour - long classes and other activities with time as a variable) and the y - axis should represent height from the ground floor (in floors or a unit of vertical distance like feet/inches, to show the floor level Aba is on).

1. Initial State: At time \(t = 0\), Aba is on the ground floor, so height \(h=0\).
2. First Movement: Walks up to the third floor (height increases) and stays for an hour (height is constant at 3rd floor level).
3. Second Movement: Goes to the basement (height decreases, basement is below ground floor, so height is negative or a lower value than 0) and stays for an hour (height constant at basement level).
4. Third Movement: Goes back to ground floor (height increases back to 0) and stays (height constant at 0) while eating lunch.

We can sketch a piece - wise function graph:

• From \(t = 0\) to \(t=t_1\) (time to reach 3rd floor), a line with positive slope from \((0,0)\) to \((t_1,3)\) (assuming 3rd floor is height 3).
• From \(t = t_1\) to \(t=t_1 + 1\) (1 - hour class), a horizontal line at \(y = 3\).
• From \(t=t_1 + 1\) to \(t=t_1+1 + t_2\) (time to reach basement), a line with negative slope from \((t_1 + 1,3)\) to \((t_1+1 + t_2,-1)\) (assuming basement is - 1).
• From \(t=t_1+1 + t_2\) to \(t=t_1+1 + t_2+1\) (1 - hour class), a horizontal line at \(y=-1\).
• From \(t=t_1+1 + t_2+1\) to \(t=t_1+1 + t_2+1 + t_3\) (time to reach ground floor), a line with positive slope from \((t_1+1 + t_2+1,-1)\) to \((t_1+1 + t_2+1 + t_3,0)\).
• From \(t=t_1+1 + t_2+1 + t_3\) onwards, a horizontal line at \(y = 0\).

• Fishing: Involves mostly standing or sitting, speed is near zero most of the time, doesn't match the speed - time graph with changes in speed.
• Skydiving: Initial speed increases (free - fall) then decreases (parachute opens), but the graph has multiple speed changes, not just two phases.
• 100 - yard sprint: In a 100 - yard sprint, the runner starts from rest, accelerates to a maximum speed, and then maybe has a slight deceleration at the end, but the graph has more than two speed peaks/troughs.
• Golf: Involves short bursts of speed (swinging) but not the continuous speed changes shown.
• Soccer: In a soccer game, a player starts from rest, accelerates (when running to the ball), decelerates (when stopping or changing direction), and has multiple periods of acceleration and deceleration as they move around the field, which matches the speed - time graph with multiple speed peaks and troughs.

Answer:

x - axis: Time (e.g., in hours/minutes); y - axis: Height from ground floor (e.g., in floors/vertical distance units)

Problem 7