Finding the range of a relation

I have troubles in working out the range of the following relations:

y=x-a, x<0, a>0

y=(a/x)+a, a>0

May you please list out the steps because I really want to understand the way~

Also:

y=square root x, x>_0 ---> Shouldn't the range be "all real numbers"? I saw the answer is [0,infinity[

(Because for example, assuming that x=81, so y=square root 81, which equals either (-9) or (9), meaning that negative numbers are also accepted, so I think it is "all real numbers") Am I right?

Re: Finding the range of a relation

Quote:

Originally Posted by

**kevinlam2490** I have troubles in working out the range of the following relations:

y=x-a, x<0, a>0

y=(a/x)+a, a>0

May you please list out the steps because I really want to understand the way~

Also:

y=square root x, x>_0 ---> Shouldn't the range be "all real numbers"? I saw the answer is [0,infinity[

(Because for example, assuming that x=81, so y=square root 81, which equals either (-9) or (9), meaning that negative numbers are also accepted, so I think it is "all real numbers") Am I right?

For the first, what would the range of $\displaystyle \displaystyle y = x$ be if you restrict $\displaystyle \displaystyle x < 0$? Then translate this graph downward $\displaystyle \displaystyle a$ units.

For the second, think of the graph $\displaystyle \displaystyle y = \frac{1}{x}$. What is the range of this graph? A dilation will not change the range, but a translation of $\displaystyle \displaystyle a$ units up will.

For the third, the square root FUNCTION is defined as $\displaystyle \displaystyle y = +\sqrt{x}$. What is the range when only the top half of the parabola is used?