Say we want to determine how many people we can invite to a party for a given budget ($ input). We want one snack and one soda for each person. The snack cost is $1 and the soda cost is $1 per can for $2 total.
How many people I can invite (the range) based on the amount of money I can spend (the domain $)? What does the function tell us for the following budgets (How many people can I invite) $100? $126?, and $166?
An example of a similar function is f(x) for the number of bus tickets I can buy for x dollars. If a bus ticket costs $2.50, then
f(x)=x/2.50
f(10)=10/2.50=4, so I can buy 4 bus tickets for $10.
You can proceed in a similar way for the party function.
To determine the range of how many people you can invite based on your budget, we need to set up a function that relates the budget ($ input) to the number of people you can invite.
Let's define the function as follows:
- Let x be the number of people you can invite.
- Let y be the budget in dollars.
Based on the given information, we know that for each person, you need $2 ($1 for snack and $1 for soda). So, the total cost (C) for inviting x number of people can be calculated as:
C = 2x
Now, to find the range of values for x (number of people you can invite) within a given budget (y), we need to solve for x in terms of y.
From the equation C = 2x, we can rearrange it to solve for x:
x = C/2
Now, we can substitute the budget (y) for C in the equation:
x = y/2
The function x = y/2 tells us the number of people you can invite based on the amount of money you can spend.
Now, let's plug in the given budgets and find out how many people you can invite for each case:
1. For a budget of $100:
x = 100/2 = 50
So, you can invite 50 people for a budget of $100.
2. For a budget of $126:
x = 126/2 = 63
So, you can invite 63 people for a budget of $126.
3. For a budget of $166:
x = 166/2 = 83
So, you can invite 83 people for a budget of $166.
Therefore, the function x = y/2 tells us how many people you can invite based on the given budgets of $100, $126, and $166.