If the relationships below are given in the form (input, output), which pairing always describes a function? (number of doors in a car, number of cup holders in the car) (height of a building in feet, height of the building in inches) (beverage charge on a bill, total meal charge on the bill) (distance from home during a trip, time elapsed during the trip)
Question
If the relationships below are given in the form (input, output), which pairing always describes a function? (number of doors in a car, number of cup holders in the car) (height of a building in feet, height of the building in inches) (beverage charge on a bill, total meal charge on the bill) (distance from home during a trip, time elapsed during the trip)
Solution
A function is a relationship between two sets of numbers where each input has exactly one output.
-
(number of doors in a car, number of cup holders in the car): This does not always describe a function because different cars with the same number of doors can have different numbers of cup holders.
-
(height of a building in feet, height of the building in inches): This always describes a function because the height of a building in inches is directly proportional to the height in feet. For every foot, there are exactly 12 inches. So, each input (height in feet) corresponds to exactly one output (height in inches).
-
(beverage charge on a bill, total meal charge on the bill): This does not always describe a function because the total meal charge can vary even if the beverage charge is the same, depending on what else is ordered.
-
(distance from home during a trip, time elapsed during the trip): This does not always describe a function because the same distance can be covered in different amounts of time, depending on speed, traffic, etc.
So, the pairing that always describes a function is (height of a building in feet, height of the building in inches).
Similar Questions
Given the sets of ordered pairs, determine if they represent a relation or a function. If it is a function,specify the domain and range. (Criteria A)a) {(1,2),(2,3),(1,5),(4,6)}{(1,2),(2,3),(1,5),(4,6)}b) {(3,4),(2,7),(5,2),(3,1)}{(3,4),(2,7),(5,2),(3,1)}c) {(2,3),(5,6),(2,7),(8,1)}{(2,3),(5,6),(2,7),(8,1)}d) {(1,3),(2,5),(3,7),(4,9)}{(1,3),(2,5),(3,7),(4,9)}
A mathematical relation is a ________________________ between two quantities.We can relate the two quantities in a relation as input and output.• In the first example, the names of students arethe __________ and their heights are the.__________Input OutputJosh 50Beth 55Casper 62Jenny 51Bob 55We can also represent a relationship graphically.• Each input is ______________ to one or moreoutputs.• called method ______________• In the relation of students and their heights,every __________ has one ____________.
Consider the following sentence:"Your monthly cash flow is a function of your income and expenses"Which of the following correctly identifies the input(s) and output(s) of this function?Group of answer choicesInputs: income and expenses; Output: monthly cash flowInput: monthly cash flow; Outputs: income and expensesInput: monthly cash flow; Output: incomeInput: monthly cash flow; Output: expensesInput: expenses; Output: income
Which of the following relations are functions?R1 ={(3, 4),(4, 5),(6, 7),(8, 9)}, R2 ={(3, 4),(4, 5),(6, 7),(3, 9)}, R3 ={(-3, 4),(4, -5),(0, 0),(8, 9)}, R4 ={(8, 11),(34, 5),(6, 17),(8, 19)}
Which set of ordered pairs does not represent a function? A (4, 1), (6, 2), (7, 5), (9, 2) B (0, 5), (1, 7), (2, 9), (3, 11) C (−2, 5), (0, 2), (9, −6), (8, 7) D (5, 5), (6, 10), (10, 15), (5, 20)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.