what is the domain, range and x-intercept of:

Question

y2-x²=0.5

Answer 1

Solve for y.

 

y² = 0.5 + x²

 

y = ±√(0.5 + x²)

 

 

Set the value under the square-root greater or equal to zero.

 

0.5 + x² ≥ 0

 

         x² ≥ -0.5

 

This is true for all value of x.  So your domain is all real numbers.  Because any value raised to an even number is positive.  Positive is greater than negative.

 

 

Now we solve for the zeros.   Set y=0.

 

0 - x² = 1/2

 

-x² = 1/2

 

x² = -1/2

 

 

Since a squared value is never negative, there are no x-intercepts.

 

To find range, take the square-root of the constant value.  The square-root of 1/2 is √(2)/2.

 

 

The range is in the interval  (-∞ , -√(2/)/2)∪(√(2)/2 , ∞).