Answer and Step by Step:
To determine the inputs and outputs for the function describing the small bus ride scenario, let's analyze it step by step:
Inputs and outputs for the function:
1. Inputs:
- Number of people taking the bus (can range from 3 to 10)
2. Outputs:
- Total cost of the ride (based on the number of people)
- Whether the bus will run (Yes, if at least 3 people take it; No, if fewer than 3)
When considering the numbers that make sense as inputs and outputs for this function:
- Inputs should include integers from 3 to 10 since the bus requires at least 3 people and can accommodate a maximum of 10 people.
- Outputs would include:
- Total cost of the ride, which is calculated as $3.50 per person.
- The bus running status, which is determined by the number of people (Yes if 3 or more people, No if fewer than 3).
By focusing on these inputs and outputs within the defined constraints of the scenario, we ensure a clear understanding of the function's behavior and relevant data points for the small bus ride from the train station to the concert.
To analyze the scenario of the small bus ride from the train station to a concert, let's break it down step by step:
A) Inputs and outputs for the function:
1. Inputs:
- Number of people taking the bus (can range from 3 to 10)
2. Outputs:
- Total cost of the ride (based on the number of people)
- Whether the bus will run (Yes, if at least 3 people take it; No, if fewer than 3)
B) Sketching a graph:
For the graph, you can have the x-axis represent the number of people taking the bus (from 3 to 10) and the y-axis represent the total cost of the ride. The graph should show a step function:
- The cost remains constant at $3.50 per person when the number of people is between 3 and 10.
- The bus will not run for fewer than 3 people (output is "No"), which can be represented by a gap in the graph for values less than 3.
- The bus runs for 3 or more people, and the cost is linearly increasing with the number of people but capped at 10 people.
By creating this graph, you visually represent the relationship between the number of people taking the bus, the total cost of the ride, and the condition for the bus to operate. It helps in understanding the function and its behavior in a clear and concise manner.
