Posted by Lori on .
I don't know which is which
y=(x+9)^23
I know it is all real numbers, but i don't know if my answer should be
[3,00)
or
(9,00)
Can some one explain this?

Algebra 
Damon,
I do not know what your question is asking for so will describe the function.
This parabola opens up (holds water) because y gets big positive as x gets big positive or negative.
The axis of symmetry, and therefore x location of the vertex, is when the quantity (x+9) is zero. That is when x is 9
For example if you go one space left and right of x = 9, you should get the same y
well if x = 91 = 10, then y = 13 = 2
and if x = 9 + 1 = 8, then y = 13 = 2 sure enough the same.
Now to find the vertex, we already know that (x+9) is zero at x = 9 so we need y there, but it is obviously 03 = 3
so the location of the vertex is (9,3) 
Algebra 
Damon,
Now about your "all real numbers" comment.
Yes, the domain of x is all real numbers, you can find a y for any old x.
However we can not find any y below the vertex at y = 3 because the whole parabola is above the vertex at (9,3)
Therefore the Range of y is y greater than or equal to 3