# Math Help - Domain & Range

1. ## Domain & Range

1. y=2e^-x -3
2. y=2sin(3x+pi) - 1
3. y= {sqrt(-x) -4 < x < 0
{sqrt(x) 0 < x < 4

domain is asking for allowable x-values and range asks for resulting y-values, but i'm not sure how to do it for these.

2. Originally Posted by fezz349
1. y=2e^-x -3
2. y=2sin(3x+pi) - 1
3. y= {sqrt(-x) -4 < x < 0
{sqrt(x) 0 < x < 4

domain is asking for allowable x-values and range asks for resulting y-values, but i'm not sure how to do it for these.
if you are unfamiliar with the behavior of each parent function and its subsequent transformation, then I recommend that you graph each equation using technology to better "see" the domain and range.

3. I know I can easily graph them in my calculator and come up with the answers but I'm interested in the algebraic breakdown.

4. Originally Posted by fezz349
I know I can easily graph them in my calculator and come up with the answers but I'm interested in the algebraic breakdown.
ok, here is the algebra thought process involved for your first function $y = 2e^{-x} - 3$ ...

what is the domain and range of the parent function $y = e^{x}$ ?

what transformation occurs to $y = e^x$ if the sign of x is changed? how does that transformation affect the domain and range?

how does the transformation of multiplying $e^{-x}$ by $2$ affect the domain and range?

finally, how does the final transformation of subtracting $3$ from $2e^{-x}$ affect the domain and range?