Simple Functions or Not Functions

May 2010
24
0
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= √x-1
y= |x|
y= 1/x
x=y^2
x+3y= x^3
x^2+y^2= 4
 
Apr 2010
384
153
Canada
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= √x-1
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!