I'm just having trouble trying to see the independent and dependant variables. I have to determine whether the following are functions:
The relation between distance and time if someone walks 5km/h. I think distance would be the independent variable because you can go different speeds and that can take more or less time? So time would be the dependant variable. So my equation would be y=5x. This would be a function.
Next, the relation between a student's age and the number of credits earned. I think that the number of credits earned would be the independent variable because a student can skip a grade or fail a grade and that would effect their age, right? I don't know how I would do an equation for this, but it says at the back of my book that this wouldn't be a function.
I'd really appreciate any help, thank you for your time!
You fixed the speed at 5
d = 5 t
distance, d, depends on how long you walk ,t
We are assuming that the number of credits earned is a function of (dependent on) age
age is independent
credits is dependent
There is no function implied here, in fact there might be multiple values of credits at a given age. A function has only one value of credits for each age.
Thank you so much for the help, this explains so much!!
To determine whether a relation is a function, we need to understand the concepts of independent and dependent variables.
In a function, one variable (usually denoted as 'x' or the independent variable) uniquely determines the value of another variable (usually denoted as 'y' or the dependent variable). The independent variable is the input, and the dependent variable is the output.
Let's analyze the examples you provided:
1. The relation between distance and time if someone walks 5km/h:
Here, distance and time are related, and we want to determine if it is a function. In this scenario, time is the independent variable because it determines the value of the distance. As the person walks at a fixed speed of 5km/h, the distance covered will depend on the time taken. Thus, distance is the dependent variable. The equation y = 5x represents this relationship, where y is the dependent variable (distance) and x is the independent variable (time). Since each value of time corresponds to a unique distance covered, this is indeed a function.
2. The relation between a student's age and the number of credits earned:
In this case, age and the number of credits earned are related, and we need to determine if it forms a function. Here, age is the independent variable because the number of credits earned can vary depending on the student's age. However, the number of credits earned cannot uniquely determine the student's age because students can earn different numbers of credits at the same age. This means that multiple ages can correspond to the same number of credits. Hence, the relation between age and the number of credits earned is not a function.
To summarize:
- In the first example, the relation between distance and time is a function, with distance as the dependent variable and time as the independent variable.
- In the second example, the relation between a student's age and the number of credits earned is not a function, as the number of credits earned does not uniquely determine the student's age.
I hope this explanation clarifies your understanding. If you have any further questions, feel free to ask!