Domain And Range

**foreverbrokenpromises** · December 11th 2009, 05:05 PM

1) State the domain and range of each of the following functions:
a) y = 3x + 4
b) y = $3(x-4)^2 +5$
c) y = √ 2x-10
(the root is over all the numbers for c)
d) y = √ $-x^2 + 4$
(the square root sign is over all the numbers for d) as well
e) y = 2 |1− x |−17
f) $y = x/ (x^2-x-6)$

Can someone help me find these plus explain why for d) e) and f)

**VonNemo19** · December 11th 2009, 05:22 PM

Originally Posted by foreverbrokenpromises

1) State the domain and range of each of the following functions:
a) y = 3x + 4
b) y = $3(x-4)^2 +5$
c) y = √ 2x-10
(the root is over all the numbers for c)
d) y = √ $-x^2 + 4$
(the square root sign is over all the numbers for d) as well
e) y = 2 |1− x |−17
f) $y = x/ (x^2-x-6)$

Can someone help me find these plus explain why for d) e) and f)

You can think of the domain as all the numbers that x is 'allowed' to be.

As in c)... You know that you can't take the square root of a negative number and get a real number. So, x can only be those numbers that make the radicand greater than or equal to zero. In other words, solve

$2x-10\geq0$

and you will have your domain.

**millerst** · December 11th 2009, 06:41 PM

(f) You cannot include in the domain where the function is undefined, therefore areas where the dominator of a rational function is equal to zero should not be included in the domain.

So the domain is (-∞, -2) U (-2, 3) U (3, ∞)

**foreverbrokenpromises** · December 12th 2009, 12:22 PM

Thanks
I've figured out a) b) and c)

but i still cant figure out how to complete the following:

d) y = √-x^2 +4
e) y = 2 |1-x|-17
f) y= $x/ (x^2-x-6)$

pls help!

**e^(i*pi)** · December 12th 2009, 12:31 PM

Originally Posted by foreverbrokenpromises

Thanks
I've figured out a) b) and c)

but i still cant figure out how to complete the following:

d) y = √-x^2 +4
e) y = 2 |1-x|-17
f) y= $x/ (x^2-x-6)$

pls help!