What is the difference between domain and range? Describe a real life situation that could be modeled by a function?
I think I understand domain and range. Domain is the x axis and range is the y axis correct?
I need help with applying it to real life.
Thank you.
Close. The domain is all the possible x values and the range is all the possible y values. *I'm sure there is a more general way of phrasing it but my english sucks sorry.*
Lets use an example y = x.
There is no restrictions such as undefines so the domain and range are all real values.
y = sqrt(x). In this case x cannot be negative. The lowest value of x that will still give us a real number is 0 and the is no max so the domain is 0 to infinity. The range cannot be lower than 0 because there is no x value that will return a number lower than 0. The max is infinity because as x goes to infinity so does y(if you don't understand what this means please ask).
A function can be very simple. Like..
The price of one apple is 10 cents. Jack wants to buy x number of apples What is the price of x apples?
Err it's crude example but I can't think of anything else right now >.<.
Just a note, one property of a function is that every x value has one and only one y value. So as long as a real life situation does not have two outcomes, it can(I believe) be model as a function.
Best of luck I hope I helped >.<"
Yes, thank you!
is the answer 2 apples.
Yes, you are correct. In the context of functions and graphs, the domain refers to the set of all possible input values (x-values), while the range refers to the set of all possible output values (y-values).
To understand domain and range in a real-life context, let's consider an example:
Real-life situation: Suppose you are running a lemonade stand during the summer. The number of cups of lemonade you sell (output) depends on the price you set for each cup (input). Let's say you charge $1.00 for each cup of lemonade.
In this scenario, you can model the relationship between the price of lemonade and the number of cups sold with a function. Let's call the input variable "price" and the output variable "cupsSold".
Function: cupsSold = f(price)
Domain: The domain would be the possible values for the "price" variable. In this situation, you have control over the price you set, so you can choose any positive value. However, it would be reasonable to limit the domain to a practical range, such as a minimum price of $0.50 and a maximum price of $3.00.
Range: The range would be the possible values for the "cupsSold" variable. As the price increases, you would expect the number of cups sold to decrease, and vice versa. Therefore, the range would consist of non-negative whole numbers (0, 1, 2, 3, and so on), representing the possible number of cups sold.
By analyzing the data from your lemonade stand, you can plot the relationship between price and cups sold on a graph. The x-axis would represent the price, and the y-axis would represent the cups sold. The graph would show how changes in price affect the number of cups sold, and the domain and range would help define the boundaries and values along each axis.
Remember, when considering real-life situations, it is important to use common sense and carefully define the limitations and practical ranges for the variables involved.