what is the domain and range of: y = Sqrt 2x - 2 ?

Question

I really don't understand Domain and Range equations. And I need help solving this.

 

Y = √2x - 2

 

Any help?

Answer 1

Domain is the set of x values in which the function is defined.  Range is the set of y values in which the function is defined.

 

Since we cannot have a negative number under the square-root

 

2x - 2 ≥ 0

 

 

Solve the inequality.

 

2x ≥ 2

 

 x ≥ 1

 

 

The domain is [1, ∞).

 

To find the range, we simply plug in all the x values into the function that are within the domain.  Another thing that is important to know is that as x gets closer to infinity, the value of y gets closer to certain constant but never reaches it.  This y value is known as the horizontal asymptote, and serves as an indicator to how low and how high the y values can reach to.

 

y = √(2(1) - 2) = √0 = 0

 

y = √(2(2) - 2)) = √2 = 1.414

 

y = √(2(3) - 2) = √4 = 2

 

y = √(2(4) - 2) = √6 = 2.449

 

 

If we keep going, the value of y increases without any bounds.  If you have a graphing calculator, you can easily confirm this.

 

Range is [0, ∞).