Math Is Fun Forum

mathland

Member

Registered: 2021-03-25

Posts: 444

y As A Function of x

Determine whether the equation represents y
as a function of x.

1. x^2 + y^2 = 4

2. x^2 − y = 9

Let me see.

Question 1

I will solve for y.

x^2 + y^2 = 4

y^2 = -x^2 + 4

sqrt{y^2} = sqrt{-x^2 + 4}

When taking the square root, two answers is the result: one is positive, the other negative.

y = -sqrt{-x^2 + 4}

y = sqrt{-x^2 + 4}

For 1, the equation does not represent y as a function of x.

You say?

Question 2

x^2 - y = 9

Solve for y.

-y = -x^2 + 9

y = (-x^2 + 4)/(-1)

y = x^2 - 4

I see that y does not lead to two different values (positive & negative) on the right side. I say the equation for 2 represents y as a function of x.

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: y As A Function of x

Both correct.

B

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: y As A Function of x

Both correct.

B

Very good.