Question

Determine whether each of the following equations
defines y as a function of x. (Do not graph.)
x + 3 = y^2

Answer 1

how do I go about figuring problems like these out? I have a few examples

Answer 2

If you see a y^2, it's not a function of x... since once you take a square root, you get a plus or minus.

Post more examples.

Answer 3

every time I see a ^ 2? not a ^3? and does it have to be y or can it be x?

Answer 4

3x^4 − 2xy = 5x

Answer 5

y^3 is fine. y^4 is not. y^5 is fine. y^6 is not. Notice a pattern?

Answer 6

x can be anything.

Answer 7

putting it simply...a function should have only a single value of y for every x

Answer 8

This is fine: 3x^4 − 2xy = 5x since you only have a y, it can be rearranged to get a single y= ...

Answer 9

ohh okay. 3x^4 − 2xy = 5x is no?

Answer 10

ohh only 1 y.

Answer 11

you can try plugging in a number and see if u are getting a single value for y or not. Note that taking square root of a number will lead 2 values...positive and negative

Answer 12

what about 39. |y| |− 2 = x

Answer 13

y^3 is fine. y^4 is not. y^5 is fine. y^6 is not. y^7 is fine. y^8 is not. y^9 is fine. Notice a pattern?

An even power on the y means when you take a root, you get a plus or minus, meaning two values of y for every x - not a function. Odd powers on y are fine.

Answer 14

|y| − 2 = x ?

Answer 15

|y| − 2 = x
becomes
|y| = x + 2

once you drop the absolute value signs, just like a square root, you get a plus or minus, like
y = x+2
OR
y = -(x+2)

Answer 16

So an absolute value on a y = not a function. Absolute value of x is a function.

Answer 17

since absolute values have two answers will they always be no?

Answer 18

Absolute values on y, yes.

Answer 19

not necessarily....only for y