Question

how do i find the domain and range for
x+5/2x-1. I know the domain should be x is not equal to 1/2. how do i find range?

Answer 1

have fun

Answer 2

set the denominator equal to 0 to find the domain

Answer 3

but maybe a little in sight would help

Answer 4

see if you can think of a number right away that this fraction can never be

Answer 5

luigi: i figured out domain. i don't know how to do range. satellite: confused

Answer 6

with a little practice you could look at this and say right away that the range cannot include \(\frac{1}{2}\) because...

Answer 7

the denominator can never be exactly twice the numerator

Answer 8

it has nothing to do with \(\frac{1}{2}\) being excluded from the domain, that is just a coincidence

Answer 9

\[\frac{2x+5}{3x-4}\] for example can never be \(\frac{2}{3}\)

Answer 10

ummm so what are you saying? anything > 1/2 for range?

Answer 11

no i am saying the range is all numbers except \(\frac{1}{2}\)

Answer 12

we can do this is a different way if you like, but it is more cumbersome

Answer 13

ok and the domain all numbers except 1/2 too? i have another problem y=6/x-10, so the domain is everything except 10, would the range be the same 10 for that too?

Answer 14

no no that is what i was trying to say, that the last one was a coincidence

Answer 15

you have
\[y=\frac{6}{x-10}\] and this has range all real numbers except for 0
why? because a fraction is only zero if the numerator is 0, and your numerator here is 6

Answer 16

ok so every number greater than 0. so let me try the next y=3x^2-24. Domain is every number except 8. Range is ??? nevermind this is not a fraction so again i'm lost.