1. Which situation is not a function?
a) the number of days d below freezing each month
b) the total cost of an item that costs x dollars with 7% sales tax
c) the number of miles driven at a constant speed of 45 miles per hour after x hours
d) the total cost of n tickets that cost $23 each
Answer is B
To determine which situation is not a function, we need to understand what a function is.
In mathematics, a function is a relationship between two sets, where each input (element in the first set) is uniquely associated with an output (element in the second set). In other words, for every value of the input, there should be exactly one corresponding value of the output.
Let's analyze the given situations:
a) The number of days d below freezing each month: This situation can be a function. For each month, there will be a unique number of days below freezing. Therefore, it satisfies the definition of a function.
b) The total cost of an item that costs x dollars with 7% sales tax: This situation is not a function because it does not provide a unique output for each input. If we consider the cost of the item as the input (x), there will be multiple possible outputs for different values of x, as the cost with sales tax will vary.
c) The number of miles driven at a constant speed of 45 miles per hour after x hours: This situation can be a function. For each value of x hours, there will be a unique number of miles driven. Therefore, it satisfies the definition of a function.
d) The total cost of n tickets that cost $23 each: This situation can be a function. For each value of n tickets, there will be a unique total cost. Therefore, it satisfies the definition of a function.
Therefore, the situation that is not a function is option B: the total cost of an item that costs x dollars with 7% sales tax.