Question

Based on data collected from 50 random people in your school regarding their height and the time it takes them to get to school, do you think the relation between a person's height (independent variable) and the time it takes the person to get to school (dependent variable) is a function?

A) Yes, there is a linear function.
B) No, there is no discernible pattern.
C) Yes, it's a non-linear function.
D) Undetermined without additional information.

Answer 1

The relationship between height and the time it takes to get to school cannot be determined to be a function without additional data. A function implies a specific kind of relation which cannot be established here based on the information provided.

Step-by-step explanation:

To determine if the relation between a person's height and the time it takes them to get to school is a function, one would need specific data regarding the relationship between these variables. The answer choice D) Undetermined without additional information, is the most appropriate as we lack the data necessary to form a conclusion about the nature of the relationship. A function is defined in mathematics as a relation in which each input is associated with exactly one output. While height is typically an independent variable and time could potentially be a dependent variable, there is no intrinsic reason to suspect a functional relationship between these two particular variables without empirical evidence.

If data were available, we would follow these steps:

1. Choose the independent and dependent variables.
2. Draw a scatter plot of the data.
3. Look for a discernible pattern or relationship.
4. Calculate the least-squares line.
5. Analyze the correlation coefficient to determine the significance.

However, without additional information, these steps cannot be completed and the question of function cannot be resolved.