Question

a teacher asked her students to think of a number, multiply by 5, and subtract the product from 20 , then she asked them to multiply the resulting difference by the number they first thougt of

a) use function notation to express the final answer in terms of the orginal number

b)determine the outputs for the input numbers 1, -1, & 7

c) determine the maximum result possible

Answer 1

Start with n. Follow the steps:

x5 = 5n
from 20 = 20 - 5n
xn = n(20-5n)

a) 20n - 5n^2
b) f(1) = 15
f(-1) = -25
f(7) = -105

c) 20n-5n^2 = 5n(4-n)
This is zero at n=0,4

It thus attains its maximum at x=2
f(2) = 20