Question

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)

Answer 1

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

We can conclude that the table represent the cube function $f(x)=x^3$.

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

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