QUESTION: Which relation is NOT a function? Okay, I think I got the answer, but I'm not sure. need help plzz?

Question

Okay, here are the choices:

1) y= 2x + 4
2) y= x^2 - 4x + 3
3) x = 3y - 2
4) x= y^2 +2y - 3

Which is NOT a function?

Okay, so
it's not number one b/c no. 1 is a function. I put the equation in my calc. and on the graph, i got a line. so i did the vertical line test and it only passes it once- so it IS a function.

not no. 2 b/c tht is a function as well. same thing- put in calc. got a parabola- vert. line test- only pass once- IT IS A FUNCT.

not no. 3 because after i solved for Y. put in calc--same thing- vert line test- passed once- so it is a function...

no 4....i do not get how to solve for Y.....i did: ADD 3 on both sides...got x +3 = y^2 + 2y...then divided by 2, got x + 3 = y^2...square root that??????? can someone help me with tht IF i did it so far....

help....again, i am supposed to tell which is not a FUNCTION and WHY?

thanks !!!!!!!!! :)
xoxo
xoxo

Answer 1

You are right. Here is a trick on number 4.

Since you cannot graph x=y^2+2y+3

You can graph y=x^2+2x+3. (switch x and y)

If you take your graph and turn your calculator 90degrees (on its side) you will see what x=y^2+2y + 3 would look like.

When you learn inverses this trick will make sense.

Answer 2

4) x= y^2 +2y - 3
y = [ -2 +/- sqrt(2^2 -4(1)(-3-x))]/2
Thus one value of x can produce two values of y which violates the definition of a function and violates the vertical line test.

Answer 3

the fourth one is not a function because for every x value, there is more than one y value (meaning it does not pass the vertical line test)

x = y^2 + 2y - 3 = (y + 3) (y-1)

can you see how there is more than one y value for every x value?

Answer 4

number 4 is not a function.. This will produce a sideways parabola, since x and y are backwards in the traditional sequence of a quadratic equation. Therefore, many values of x will have two values of y.

Answer 5

try factoroing it