Question

Another question about domains and range
how would I find the range of (3x-4)/(6x-1) ? Without using a graph

the domain is x can't be 1/6

What is the range?

Answer 1

without using a graph

Answer 2

The range is how high or how low your graph can go
So look at what happens when you use large values of x
e.g. in your mind try x = 100 000
so you would have 299 996/599 999
For all practical purposes this is 3/6 or 1/2, even though you will never reach it.
As a matter of fact try it on your calculator you will get .49999... , in other words, less than 1/2
The larger the value of x, the closer we will get to 1/2

If we try large negative values of x
say, x = -100 000
then our calculation is -300 006/-600 001
which is slightly over .5

so no value of x will produce a y equal to 1/2

so the domain is the set of all real values of y ,except y = .5

(if you try to solve
(3x-4)/(6x-1) = 1/2
we get
6x - 8 = 6x-1
-8 = -1 which is false and a contradiction.
So there is no solution)

Answer 3

1. Use a calculator to approximate the square root of 320. Round to three decimal places