MathMaster logo

MathMaster

  1. Home
  2. general
  3. describe a real life situation that can be modeled by a function a relation in which every input value corresponds to only
Question

Describe a real-life situation that can be modeled by a function (a relation in which every input value corresponds to only one output value). The situation must be different from the examples provided in the reading and in the homework. Identify the input value and the output value of the function, and provide justification that your relation does, in fact, represent a function. 2. Create a function in the form y = f(x) that models the relation described. You may choose variables in place of y or x that better represent the relation, as seen in the provided example. 3. Identify the domain and range of your function, using proper mathematical notation.

251

likes
1254 views

Answer to a math question Describe a real-life situation that can be modeled by a function (a relation in which every input value corresponds to only one output value). The situation must be different from the examples provided in the reading and in the homework. Identify the input value and the output value of the function, and provide justification that your relation does, in fact, represent a function. 2. Create a function in the form y = f(x) that models the relation described. You may choose variables in place of y or x that better represent the relation, as seen in the provided example. 3. Identify the domain and range of your function, using proper mathematical notation.

Expert avatar
Nash
4.9
87 Answers
Real-life Situation:
A car rental company charges a fixed fee for renting a car for a certain number of days, and an additional daily rate for any extra days beyond the initial rental period.

Function Representation:
Let's say we have a car rental company that charges a fixed fee of $50 for renting a car for up to 3 days, and an additional $10 per day for any extra days beyond the initial rental period.

Input and Output Values:
In this situation, the input value would be the number of days a car is rented for, denoted by x. The output value would be the total cost of renting the car for those number of days, denoted by y.

Function Representation:
To create a function that models this relationship, we can use the piecewise function notation:

y = \begin{cases} 50 & \text{if } x \leq 3 \ 50 + 10(x-3) & \text{if } x > 3 \end{cases}

This function can be read as follows: for x less than or equal to 3, the cost of renting the car is $50. For x greater than 3, the cost is $50 plus $10 for each extra day beyond 3.

Domain and Range:
The domain of this function would be the set of possible values for x, which in this case would be the set of positive integers representing the number of days a car is rented for: D = \{1, 2, 3, 4, 5, ...\}

The range of this function would be the set of possible values for y, which in this case would be the set of positive integers representing the total cost of renting a car for a given number of days: R = \{50, 60, 70, 80, ...\}

Answer: The real-life situation of a car rental company can be modeled by the function y = \begin{cases} 50 & \text{if } x \leq 3 \ 50 + 10(x-3) & \text{if } x > 3 \end{cases} . The domain is D = \{1, 2, 3, 4, 5, ...\} and the range is R = \{50, 60, 70, 80, ...\} .

Frequently asked questions (FAQs)
What is the period of the trigonometric function y = 3sin(2x) - 5cos(5x)?
+
Math question: Find the limit as x approaches 0 of (sin(x)-x)/((x^3)*(sin(2x))).
+
What is the value of sine squared theta plus cosine squared theta?
+
New questions in Mathematics
The sum of an infinite geometric series is 13,5 The sum of the same series, calculated from the third term is 1,5. Q. Calculate r if r>0.
Consider the relation R defined on the set of positive integers as (x,y) ∈ R if x divides y. Choose all the true statements. R is reflexive. R is symmetric. R is antisymmetric. R is transitive. R is a partial order. R is a total order. R is an equivalence relation.
Use the elimination to find the solution to each linear system. X+y=43 2x-y=20
A company is wondering whether to invest £18,000 in a project which would make extra profits of £10,009 in the first year, £8,000 in the second year and £6,000 in the third year. It’s cost of capital is 10% (in other words, it would require a return of at least 10% on its investment). You are required to evaluate the project.
(6.2x10^3)(3x10^-6)
Determine the absolute extrema of the function 𝑓(𝑥)=𝑥3−18𝑥2 96𝑥 , on the interval [1,10]
Find the root of x^4-10x^ 5=0 using Newton's method, with a precision of the smallest positive root.
You are planning to buy a car worth $20,000. Which of the two deals described below would you choose, both with a 48-month term? (NB: estimate the monthly payment of each offer). i) the dealer offers to take 10% off the price, then lend you the balance at an annual percentage rate (APR) of 9%, monthly compounding. ii) the dealer offers to lend you $20,000 (i.e., no discount) at an APR of 3%, monthly compounding.
2x2 and how much?
A person borrows rm 1000 from a bank at an interest rate of 10%. After some time, he pays the bank rm 1900 as full and final settlement of the loan. Estimate the duration of his loan.
4x/2+5x-3/6=7/8-1/4-x
The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations. 84. Find the probability that the average price for 30 gas stations is less than $4.55. a 0.6554 b 0.3446 c 0.0142 d 0.9858 e 0
Find all real numbers x that satisfy the equation \sqrt{x^2-2}=\sqrt{3-x}
Fill in the P(X-x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -5 ,3 , 4, 5 , and 6.
In poker, a full house consists of five cards, where two of the cards have the same number (or letter) and the remaining three also have the same number (or letter) as each other (but not as the previous two cards). Use a search engine or Wikipedia to understand the concept better if necessary. In how many different ways can one obtain a full house?
The area bounded by the curve y=ln(x) and the lines x=1 and x=4 above the x−axis is
Below are three 95% CIs (where 𝜎 was known and 𝑥̅happened to be the same); one with sample size 30, one with samplesize 40, and one with sample size 50. Which is which?(66.2, 76.2)(61.2, 81.2)(56.2, 86.2)
a) 6x − 5 > x + 20
7-1=6 6x2=12 Explain that
If the area of a circle is 75.7ft2, what is the radius? Give the answer in metres. Round answer to 2 decimal places and enter the units.

You might be interested in