Ineed with this last problem. algebra 2

g(x)  = (x-2) ^ 1/3 +5

Step-by-step explanation:

f(x) = x^1/3

We want to shift it 2 units to the right

h(x) = f(x+c) where   c<0 to move it to the right

                         To move it 2 units to the right  c =-2

h(x) = f(x-2)

Substitute x-2 in for x in the function

h(x) = (x-2) ^ 1/3

Now we want to shift it 5 units up

g(x) = h(x)+c where   c>0 to move it up

                         To move it 5 units up  c =5

g(x) = h(x)+5

g(x)  = (x-2) ^ 1/3 +5

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).