hey guys, i needed help on determining how to understand if these are functions or not? I already have the answers, but i dont know how to figure it out
y=x+1
y= 3x^2
y= √x1
y= x
y= 1/x
x=y^2
x+3y= x^3
x^2+y^2= 4
Can you define function?
function assigns a unique value to each input of a specified type.

http://en.wikipedia.org/wiki/Function_(mathematics)
Which means we need to express all of the above in the form
\(\displaystyle y=f(x) \)
And see which ones offer 2 values of y for 1 value of x.
Let's go through the list
\(\displaystyle y=x+1\)
Function
\(\displaystyle y= 3x^2 \)
Function
\(\displaystyle y= \sqrt(x) 1\)
Not a funtion because there are 2 values of y for every value of x.
...and so on and so fourth
Note that all we are doing here is the "vertical line test" which means if we make a vertical tangent to any point on the curve it only touches the curve once!