# Domain And Range

• Dec 11th 2009, 05:05 PM
foreverbrokenpromises
Domain And Range
1) State the domain and range of each of the following functions:
a) y = 3x + 4
b) y = $\displaystyle 3(x-4)^2 +5$
c) y = √ 2x-10
(the root is over all the numbers for c)
d) y = √ $\displaystyle -x^2 + 4$
(the square root sign is over all the numbers for d) as well
e) y = 2 |1x |17
f) $\displaystyle y = x/ (x^2-x-6)$

Can someone help me find these plus explain why for d) e) and f)
• Dec 11th 2009, 05:22 PM
VonNemo19
Quote:

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

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

$\displaystyle 2x-10\geq0$

and you will have your domain.
• Dec 11th 2009, 06:41 PM
millerst
(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, ∞)
• Dec 12th 2009, 12:22 PM
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= $\displaystyle x/ (x^2-x-6)$

pls help!
• Dec 12th 2009, 12:31 PM
e^(i*pi)
Quote:

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= $\displaystyle x/ (x^2-x-6)$

pls help!

For d apply the principle VonNemo19 outlined in post 2.

d) $\displaystyle -x^2+4 \geq 0 \: \: \rightarrow \: \: 4-x^2 \geq 0$

$\displaystyle (2-x)(2+x) \geq 0$.

Spoiler:
$\displaystyle -2 \leq x \leq 2$

e) What values of x are not allowed in this linear equation?

Spoiler:
There are none so x is all the real numbers

f) $\displaystyle x^2-x-6=(x+2)(x-3)$. Remember that any value that makes the denominator equal to 0 is not allowed

Spoiler:
$\displaystyle x \in \mathbb{R} \: , \: x \neq -2,3$