Y as a Function of X: Deciding the Equation

[AznBoi]

Hmm I'm not sure if this is correct:

Problem: Decide whether the equation represents y as a function of x:

y=sq.rt.(x+3)

Ok, so do square roots always have the plus/minus sign automatically? Radicals are the equivalent of sleep parabolas right?? Do I add the bottom half also??

My answer was No because it is a radical/sleeping parabola.

 

[HallsofIvy]

Hmm I'm not sure if this is correct:

Problem: Decide whether the equation represents y as a function of x:

y=sq.rt.(x+3)

Ok, so do square roots always have the plus/minus sign automatically?

No, \sqrt{x} is defined as the positive number whose square is equal to x. Square root, like any real valued function, is single valued.

Radicals are the equivalent of sleep parabolas right?? Do I add the bottom half also??

My answer was No because it is a radical/sleeping parabola.

"Sleeping" parabola? You mean a parabola with its axis horizontal?
Unfortunately, you are wrong. \sqrt{x+3} is a function. It's graph is the top half of the horizontal parabola.

 

[courtrigrad]

it is a function because it passes the vertical line test. usually the square root means the principal square root.

 

[AznBoi]

ok thanks.