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)
Math question: What is the factored form of the quadratic equation x^2 + 7x + 10?
+
What is the average temperature (in degrees Celsius) of a city over the past 7 days if the recorded temperatures were 32, 34, 28, 31, 30, 29, and 33?
+
Question: Find the value of sin(45°) + cos(45°)
+
New questions in Mathematics
A hotel in the Algarve had to offer 1 week of vacation to one of its employees as an Easter gift in a random choice. It is known that 80 people work in this hotel unit, 41 of whom are Portuguese and 39 are foreign nationals. There are 14 Portuguese men and 23 foreign women. Using what you know about conditional probability, check the probability that the gift was offered to a Portuguese citizen, knowing that it was a woman.
Find the equation of the normal to the curve y=x²+4x-3 at point(1,2)
Answer the following questions regarding the expression below. 0.1 (a) Write the number as a fraction.
What is the r.p.m. required to drill a 13/16" hole in mild steel if the cutting speed is 100 feet per minute?
how many arrangement can be made of 4 letters chosen from the 8 letters of the world ABBSOLUTE
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.
Convert 78 percent to a decimal
4x/2+5x-3/6=7/8-1/4-x
What’s the slope of a tangent line at x=1 for f(x)=x2. We can find the slopes of a sequence of secant lines that get closer and closer to the tangent line. What we are working towards is the process of finding a “limit” which is a foundational topic of calculus.
3/9*4/8=
X³-27
Twenty‐five students in a class take a test for which the average grade is 75. Then a twenty‐sixth student enters the class, takes the same test, and scores 70. The test average grade calculated with 26 students will
a survey showed that 3 out of 7 voters would vote in an election. based on this survey, how many people would vote in a city with 25,000 people?
(6²-14)÷11•(-3)
How many cards do you expect to pull from a poker deck until you get an ACE?
25) Paulo saves R$250.00 per month and keeps the money in a safe in his own home. At the end of 12 months, deposit the total saved into the savings account. Consider that, each year, deposits are always carried out on the same day and month; the annual yield on the savings account is 7%; and, the yield total is obtained by the interest compounding process. So, the amount that Paulo will have in his savings account after 3 years, from the moment you started saving part of your money monthly, it will be A) R$6,644.70. B) R$ 9,210.00. C) R$ 9,644.70. D) R$ 10,319.83. E) R$ 13,319.83
16-(x²+x+2)²
Kayla started a book club at her school. The number of girls in the book club was one more than twice the number of boys. If there are 15 girls in the book club, how many boys are in the club?
-Please answer to the following questions: What is the price elasticity of demand? Can you explain it in your own words? What is the price elasticity of supply? Can you explain it in your own words? What is the relationship between price elasticity and position on the demand curve? For example, as you move up the demand curve to higher prices and lower quantities, what happens to the measured elasticity? How would you explain that? B-Assume that the supply of low-skilled workers is fairly elastic, but the employers’ demand for such workers is fairly inelastic. If the policy goal is to expand employment for low-skilled workers, is it better to focus on policy tools to shift the supply of unskilled labor or on tools to shift the demand for unskilled labor? What if the policy goal is to raise wages for this group? Explain your answers with supply and demand diagrams. Make sure to properly cite and reference your academic or peer-reviewed sources (minimum 2).
f(x)= 9-x^2 find (f(x+h)-f(x) )/h

You might be interested in