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
85 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)
Find the x-values for which the tangent function, f(x) = tan(x), has a vertical asymptote.
+
What is the probability of getting a sum of 7 when rolling two fair six-sided dice?
+
What is the product of 87 multiplied by 42?
+
New questions in Mathematics
Calculate to represent the function whose graph is a line that passes through the points (1,2) and (−3,4). What is your slope?
a to the power of 2 minus 16 over a plus 4, what is the result?
-11+29-18
3x+2/2x-1 + 3+x/2x-1 - 3x-2/2x-1
(3x^(2) 9x 6)/(5x^(2)-20)
How many anagrams of the word STROMEC there that do not contain STROM, MOST, MOC or CEST as a subword? By subword is meant anything that is created by omitting some letters - for example, the word EMROSCT contains both MOC and MOST as subwords.
A merchant can sell 20 electric shavers a day at a price of 25 each, but he can sell 30 if he sets a price of 20 for each electric shaver. Determine the demand equation, assuming it is linear. Consider (P= price, X= quantity demanded)
Let r: x - y 5 = 0. Determine a general equation of the line s parallel to the line r, which forms an isosceles triangle with area 8 with the line x = 5 and the Ox axis.
Given (3x+2)E [2;14] how much money (in soles) does Sophia have if numerically it is the greatest value of x?
19) If the temperature of -8°C decreases by 12°C, how much will it be? a)-20°C -4°C c) 4°C d) 20°C
I. Order to add 40.25+1.31+.45 what is the first action to do ?
The simple average of 15 , 30 , 40 , and 45 is
From 1975 through 2020 the mean annual gain of the Dow Jones Industrial Average was 652. A random sample of 34 years is selected from this population. What is the probability that the mean gain for the sample was between 400 and 800? Assume the standard deviation is 1539
User One of the applications of the derivative of a function is its use in Physics, where a function that at every instant t associates the number s(t), this function s is called the clockwise function of the movement. By deriving the time function we obtain the velocity function at time t, denoted by v(t). A body has a time function that determines its position in meters at time t as S(t)=t.³√t+2.t . Present the speed of this body at time t = 8 s.
For what values of m is point P (m, 1 - 2m) in the 2⁰ quadrant?
A hardware bill totals $857.63 with discounts of 5% and 3%. What is the net cost of the Material ?
Given a circle 𝑘(𝑆; 𝑟 = 4 𝑐𝑚) and a line |𝐴𝐵| = 2 𝑐𝑚. Determine and construct the set of all centers of circles that touch circle 𝑘 and have radius 𝑟 = |𝐴𝐵|
How much does 7.2 moles of ammonium dichromate weigh? (NH4)2Cr2O7
Solve the following system of equations using substitution. y=-4x- 11. 3x+7y=-2
Exercise The temperature T in degrees Celsius of a chemical reaction is given as a function of time t, expressed in minutes, by the function defined on ¿ by: T (t )=(20 t +10)e−0.5t. 1) What is the initial temperature? 2) Show that T' (t )=(−10 t +15)e−0 .5t. 3) Study the sign of T' (t ), then draw up the table of variations of T . We do not ask for the limit of T in +∞. 4) What is the maximum temperature reached by the reaction chemical. We will give an approximate value to within 10−2. 5) After how long does the temperature T go back down to its initial value? We will give an approximate value of this time in minutes and seconds. DM 2: study of a function Exercise The temperature T in degrees Celsius of a chemical reaction is given as a function of time t, expressed in minutes, by the function defined on ¿ by: T (t )=(20 t +10)e−0.5t. 1) What is the initial temperature? 2) Show that T' (t )=(−10 t +15)e−0.5 t. 3) Study the sign of T' (t ), then draw up the table of variations of T . We do not ask for the limit of T in +∞. 4) What is the maximum temperature reached by the reaction chemical. We will give an approximate value to within 10−2. 5) After how long does the temperature T go back down to its initial value? We will give an approximate value of this time in minutes and seconds.

You might be interested in