# Domain/Range and Absolute values

• Feb 8th 2009, 02:41 PM
Skoz
Domain/Range and Absolute values
1.) state the domain and range of each relation, then determine if the relation is a function.

a) y= -2(x+1)^2-3

b) y=1/x+3

c) 2sinx

2.) Evaluate

a) l-22l / l-11l + -16/ l-4l
• Feb 8th 2009, 04:25 PM
ThePerfectHacker
Quote:

Originally Posted by Skoz
1.) state the domain and range of each relation, then determine if the relation is a function.

a) y= -2(x+1)^2-3

The domain are all real x.
Remember that $\displaystyle (x+1)^2\geq 0 \implies -2(x+1)^2 \leq 0 \implies -2(x+1)^2 \leq -3$ so the range is $\displaystyle y\leq -3$.

Quote:

b) y=1/x+3
The domain are all $\displaystyle x\not = 0$.
As for the range we have $\displaystyle y>3 \text{ or }y<-3$.
To see this picture the hyperbola $\displaystyle y=x$ and shift it up 3 units.

Quote:

c) 2sinx
The domain are all real x and remember that $\displaystyle -1\leq \sin x\leq 1 \implies -2\leq 2\sin x\leq 2$.
Thus, range is $\displaystyle |y|\leq 2$.