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.

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- Sep 7th 2009, 09:04 AMfezz349Domain & 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. - Sep 7th 2009, 09:37 AMskeeter
- Sep 7th 2009, 10:53 AMfezz349
I know I can easily graph them in my calculator and come up with the answers but I'm interested in the algebraic breakdown.

- Sep 7th 2009, 11:05 AMskeeter
ok, here is the algebra thought process involved for your first function $\displaystyle y = 2e^{-x} - 3$ ...

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

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

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

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