WILL REWARD BRAINLIEST! The table below shows the cubes of different numbers: Number (x) 3 −3 5 −5 Cube of the number (y) 27 −27 125 −125

Part A: Does the table represent y as a function of x? Justify your answer. (5 points) Part B: The total cost f(x), in dollars, for renting a car for x days is shown below: f(x) = 27x + 18 What is the value of f(6) and what does f(6) represent? (5 points)

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07-04-2018
Mathematics

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WILL REWARD BRAINLIEST! The table below shows the cubes of different numbers: Number (x) 3 −3 5 −5 Cube of the number (y) 27 −27 125 −125

Part A: Does the table represent y as a function of x? Justify your answer. (5 points) Part B: The total cost f(x), in dollars, for renting a car for x days is shown below: f(x) = 27x + 18 What is the value of f(6) and what does f(6) represent? (5 points)

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Part A. Notice that [tex]3^3=27[/tex], [tex]-3^3=-27[/tex], [tex]5^3=125[/tex], and [tex]-5^3=-125[/tex]. If we let [tex]x[/tex] represent the number that is being cubed and [tex]f(x)[/tex] the result of that operation, we can create the function [tex]f(x)=x^3[/tex] whose domain and range are the set of all real numbers.

We can conclude that the table represent the cube function [tex]f(x)=x^3[/tex].

Part B. To find the value of [tex]f(6)[/tex], we just need to evaluate the total cost function [tex]f(x)=27x+18[/tex] at [tex]x=6[/tex]; in other word, we are going to replace [tex]x[/tex] with 6 in the function:
[tex]f(x)=27x+18[/tex]
[tex]f(6)=27(6)+18[/tex]
[tex]f(6)=162+18[/tex]
[tex]f(6)=180[/tex]
Since [tex]x[/tex] represent the number of days you are going to rent a car, it [tex]f(6)[/tex] represent the cost of renting a car for 6 days.

We can conclude that the value of [tex]f(6)[/tex] is $180, and it represent the cost of renting a car for 6 days.