Question

y=sq.rt.(x-4). Find domain and range.

Answer 1

\[y=\sqrt{x-4}\]

Answer 2

hint for domain:

the radicand has to be greater than or equal to zero so do \[x - 4 \ge 0\] then solve for x

Answer 3

does that help?

Answer 4

so the domain is just \[x \ge 4\]?

Answer 5

Yes that means that x can be anything equal to or greater than 4. The reason for this is because we can't have a negative value inside the square root. This will give us an imaginary number

Answer 6

The lowest number that x can be is 4 right? What do you get for y when you plug in x=4 into\[y=\sqrt{x−4}\]

Answer 7

0

Answer 8

so anyway...that was the domain...

Answer 9

now to find the range...solve for x

Answer 10

do you know how to? or do you need help?

Answer 11

great we know that the lowest value of y is 0 and we know that we can plug any value greater than 4 until infinity

so the range is from
\[0 \rightarrow \infty \]

Answer 12

This means y can be any number as long as it's positive. I don't know the proper notation for this can you help out @lgbasallote

Answer 13

hmm for a proper solution to find the range...solve for x

start by squaring both sides
\[y^2 = x - 4\]
add 4 to both sides
\[y^2 + 4 = x\]
since there are no restrictions for this term, the range is actually from \(-\infty\) to \(\infty\) <--that means all real values

Answer 14

since there are no restrictions for this equation*

Answer 15

I thought it was restricted.....from the domain

Answer 16

well square roots have positive and negative roots right?

Answer 17

the domain says that values of x have to be greater than 4

Answer 18

no you can't have a negative outcome from a square root.

Answer 19

that's why it's wiser to *solve* for x to avoid confusion hehe

Answer 20

\[\sqrt 4 = \pm 2\]

Answer 21

because 2^2 is 4 and (-2)^2 is also 4

Answer 22

the positive root is just the prinicipal root

Answer 23

when you graph it, the line starts at (4,0) and continues onward (infinite). so wouldn't it be \[(0, \infty)\]?

Answer 24

what number do you plug in for x in order to get -2?

Answer 25

if you plug in 8 you will get \[\sqrt 4\] that is equal to 2 and -2

Answer 26

the square root of 4 does not equal -2

Answer 27

(-2)^2= 4
-2 x -2 = 4

Answer 28

The domain restricts our range. Because we can't plug in anything lower than 4 into the equation the range is therefor restricted by 4 into infinity. That is why we find out what value we get for y when x=4.