SOLUTION: The daily profit of a bicycle store can be modeled by f(x)=x^3-5x^2+2x+2 where x is the number of bicycles sold. Let g(x)=f(x-4). Find the rule for g, and explain the meaning of th

Question 550504: The daily profit of a bicycle store can be modeled by f(x)=x^3-5x^2+2x+2 where x is the number of bicycles sold. Let g(x)=f(x-4). Find the rule for g, and explain the meaning of the transformation in terms of daily profit.
Choose one:
a. g(x)=x^3-5x^2+2x+6. The shop makes the same profit after selling 4 fewer bicycles.
b. g(x)=x^3+7x^2+10x-6. The shop makes the same profit after selling 4 more bicycles.
c. g(x)=x^3+7x^2+10x-6. The shop makes the same profit after selling 4 fewer bicycles
d. g(x)=x^3-5x^2+2x+6. The shop makes the same profit after selling 4 more bicycles.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The daily profit of a bicycle store can be modeled by f(x)=x^3-5x^2+2x+2 where x is the number of bicycles sold. Let g(x)=f(x-4). Find the rule for g, and explain the meaning of the transformation in terms of daily profit.
Choose one:
g(x) = f(x-4) = (x-4)^3 - 5(x-4)^2 + 2(x-4) + 2
-----
g(x) = x^3 + 3x^2(-4) + 3x(-4)^2 + (-4)^3 - 5[x^2-8x+16] + 2x-8 + 2
------
= x^3 -12x^2 +48x - 64 - 5x^2 + 40x - 80 + 2x - 6
------
= x^3 -17x^2 + 90x - 150
------
g(x) is the profit when x-4 bikes are sold.
Shop profit when 4 fewer bikes are sold.
===========================
Cheers,
Stan H.
=======================
a.. g(x)=x^3-5x^2+2x+6. The shop makes the same profit after selling 4 fewer bicycles.
b. g(x)=x^3+7x^2+10x-6. The shop makes the same profit after selling 4 more bicycles.
c. g(x)=x^3+7x^2+10x-6. The shop makes the same profit after selling 4 fewer bicycles
d. g(x)=x^3-5x^2+2x+6. The shop makes the same profit after selling 4 more bicycles.

RELATED QUESTIONS
The monthly profit, P, in thousands of dollars, of a bicycle company can be estimated by... (answered by Nate)

Al calculated the profit from his candy shop is given by the formula... (answered by solver91311)

A company that manufactures bicycle frames has determined that the monthly profit (in... (answered by lynnlo)

An automobile manufacturer can produce up to 300 cars per day. The profit made from the... (answered by Theo)

Urgent Response. Can a tutor be so kind to help with solving this problem? AKI's... (answered by ankor@dixie-net.com)

Please Help! The cost (C) of selling x calculators in a store is modeled by the... (answered by solver91311)

The profit P, in dollars, gained by selling x computers is modeled by the equation P =... (answered by jim_thompson5910)

The profit P, in dollars, gained by selling x computers is modeled by the equation... (answered by Boreal)

Please help me to solve this problem. The daily profit for the garden department of a... (answered by lwsshak3)