What is the function rule for the following situation? Rex paid $2o for a membership to the pool and pays $3.00 each time he goes to the pool. Show your work.
A. y = 20x + 3.
B. 20 = 3x +y.
C. y = x + 20.
D. None of these.
y = 20 + 3x. seems like bot put the x on the fixed cost when it belongs on the variable cost. Theres no answer choice out of the ones listed that matches the equation, so D
A. y = 20x + 3 (where y represents Rex's total cost and x represents the number of times he goes to the pool).
To show the work:
- Rex pays $20 for the membership, which is a fixed cost that doesn't change based on the number of times he goes to the pool. This can be represented by the constant term in the function rule, which is 20.
- Rex also pays $3.00 each time he goes to the pool, which is a variable cost that depends on the number of times he goes. This can be represented by the coefficient of x in the function rule, which is 3.
- Combining these, we get the function rule y = 20x + 3, which tells us Rex's total cost (y) based on the number of times he goes to the pool (x).
You are correct that the equation should be y = 20 + 3x, and that Bot must have made an error in the function rule given. However, given that none of the answer choices match the correct function rule, it is indeed appropriate to choose answer choice D, which states that none of the given options are correct. Thank you for catching that mistake!
To find the function rule, we need to understand the relationship between the total cost (y) and the number of times Rex goes to the pool (x).
We are given that Rex paid $20 for a membership to the pool, which is a fixed cost that does not change with the number of visits. This fixed cost can be represented as a constant term.
Rex also pays $3.00 each time he goes to the pool, which is a variable cost that changes with the number of visits. This variable cost can be represented by a multiple of the number of visits.
Therefore, the function rule can be represented as:
y = mx + b,
where:
- y represents the total cost,
- x represents the number of visits,
- m represents the rate of change (which is the cost per visit),
- b represents the fixed cost.
In this case, the fixed cost is $20 (b = 20) and the cost per visit is $3.00 (m = 3).
Plugging in the values, we get:
y = 3x + 20.
So, the correct function rule for this situation is A. y = 20x + 3.