1) table
x | 3 9 13 20
y | 9 27 29 60
Probe the ratio y / x
9 / 3 = 3
27 / 9 = 3
29 / 13 = 3
60 / 20 = 3
Answer: since y/ x = constant, we proved that the varibles are in direct variaton.
The function is found by doing y / x = k => y = kx
We have found k = 3, so the function is y = 3x
Answer: y = 3x
2) You can notice that y = 1 /x is the parent function of y = 5 / (x +6).
That means that you can tranform the graph of 1/x with some simple transformations (scaling and translating) to obtain the function 5/(x + 6).
If you call f(x) = 1 /x and g(x) = 5 / (x + 6), you can obtain:
g(x) = 5 * 1(x +6) = 5 * f(x+6)
That means, that the graph of g(x) is obtained by shifting the graph of f(x) 6 units to the left and scaling by tactor 5.<------------ answer.
3) The cost per share, C is equal to the cost of the table ($500) divided by the total number of contributors.
The total number of contributor is equal to 5 plus the additinal contributors, n.
The, you can do:
500 500
C = -------------------------------- = ----------
number of contributors 5 + n
So the asked function is C(n) = 500 / (5 + n) <---------answer
To find how many new contributors Jane has to recruit fo make the cost per share equal to $20, solve the equation:
500 / (5 + n) = 20
=> 500 = 20(5 + n)
=> 500 = 100 + 20n
=> 20 n = 500 - 100
=> 20 n = 400
=> n = 400 / 20
=> n = 20
Answer: 20 new contributors.
