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

Click here to see ALL problems on Expressions-with-variables

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.