Question

Does the following equation determine y to be a function of x? y square=x+3

Answer 1

Answer:

∴ y² = x + 3 is not a function

Step-by-step explanation:

* Lets explain how to solve the problem

- The definition of the function is every input (x) has only one

  output (y)

- Ex:

# y = x + 1 where x ∈ R , is a function because every x has only

  one value of y

# y² = x where x ∈ R , is not a function because y = ±√x, then one

  x has two values of y

* Lets solve the problem

∵ y² = x + 3

- Find y by taking √ for both sides

∴ y = ± √(x + 3)

- That means y = √(x + 3)  and y = - √(x + 3)

∵ (x + 3) must be greater than or equal zero because there is no

  square root for negative number

∴ x + 3 ≥ 0 ⇒ subtract 3 from both sides

∴ x ≥ -3

∴ x must be any number greater than or equal -3

- Let x = 0

∴ y = √(0 + 3) = √3 and y = - √(0 + 3) = -√3

∴ x = 0 has two values of y ⇒ y = √3 and y = -√3

- Any value of x greater than or equal 3 will have two values of y

∴ y² = x + 3 is not a function