Question

are the following a function

1. y=x/2
my guess is yes
2. y=2x+1
my guess is yes
3.y=x^2
my guess is yes
4.y=mx+b
im not sure

Answer 1

all are functions.

For #4, suppose that u and v produce the same y value. That is,

mu+b = mv+b
then that means that
mu = mv
u = v
In other words, if you have the same y-value, it can only be produced by one x-value. That means that you have a function.